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Liu–Murakami creep damage model is improved to predict the creep life of various cracked specimens. The modified creep damage law is implemented in the framework of extended finite element method (XFEM) for performing elasto-plastic creep crack growth simulations. Experiments show that the crack tip constraints vary from component to component which leads to variation in crack growth rates. A stress triaxiality function is introduced in the modified Liu–Murakami damage model to address the variation in crack growth rates. Moreover, a new definition of stress triaxiality (ratio of a linear combination of maximum principal stress and hydrostatic stress to von Mises stress) is proposed based on Leckie and Hayhurst failure criterion. The new definition of stress triaxiality is a key parameter in the prediction of time to failure. The modified Liu–Murakami creep damage model is used for the creep crack growth (CCG) simulations of several specimens under different loading conditions. Parametric studies are also performed to study the influence of various parameters on the CCG. Moreover, a combined framework of continuum damage mechanics and XFEM is used to predict the CCG life of a turbine blade. This work establishes that the modified Liu–Murakami creep damage law accurately predicts the creep life of cracked components under different constraint conditions. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To accurately simulate the collapse process of long-span spatial grid structures, certain key parameters should be treated carefully. In the present study, the effects of the strain rate and the damage and fracture parameters were analyzed. A numerical simulation shows the following information: (1) First, the Cowper-Symonds model is utilized to simulate the rate-dependent material properties, illustrating that the strain rate effect can be overlooked for a progressive collapse simulation. (2) Then, the constant failure strain method is used for a damage and fracture simulation. The first fracture of the members is postponed, and the final failure patterns are therefore quite different with an increase in the initial damage-equivalent plastic strain. (3) And, the progressive collapse pattern is unaffected while the fracture is delayed or prevented with a greater equivalent plastic strain of the final failure. These results can provide a reference for determining the damage and fracture parameters. (4) Finally, the equivalent plastic strain of the initial damage is relevant to the stress triaxiality. After considering the stress triaxiality, there is a significant difference compared with the constant failure strain model. The stress triaxiality must therefore be considered. [ABSTRACT FROM AUTHOR]

Fracture of an anisotropic rare-earth-containing magnesium alloy (ZEK100) sheet is investigated at different stress states and strain rates. A variety of sample geometries, loading conditions, and loading orientations are used to achieve different stress triaxiality and deformation mechanisms. Digital image correlation (DIC) technique is used to measure the surface strains up to fracture for all the specimens. We show that ZEK100 exhibits larger strain at fracture across the gage section of the test specimens aligned with the transverse direction (TD) than specimens aligned with the rolling direction (RD); however, the opposite is shown for the local strain measurements at fracture. With an increase in the strain rate, the strains at fracture decrease for all loading paths. A crystal plasticity finite element model is used to simulate the local stress state and deformation mechanisms for each loading condition. ZEK100 exhibits an anisotropic fracture behavior that is a function of the stress triaxiality and Lode parameter. We show that extension twinning also plays an important role in the fracture response of ZEK100. Overall, the local effective strain at fracture is lower for the specimens that exhibit the largest volume fraction of extension twinning. A novel anisotropic extension to the Hosford-Coulomb (HC) fracture model is then developed to account for the effect of extension twinning on the anisotropic fracture response of ZEK100. Image 1 • Fracture of ZEK100 is dependent on the stress state, strain rate, and the activity of different deformation mechanisms. • Extension twinning improves the hardening capability of magnesium which improves the macroscopic ductility. • The local strain at fracture was the lowest for the specimens that exhibited large volume fraction of extension twinning. • A novel anisotropic extension to a fracture initiation model was developed to account for the role of twinning on fracture. [ABSTRACT FROM AUTHOR]

This study develops a finite element analysis model to predict the ultimate strength of the base metal block shear fracture based on previous experimental results and compares the experimental results with the analysis results to verify the effectiveness of the analysis model. This study also analyzed additional variables of the welding direction and weld length on the applied load to investigate the structural behaviors and fracture conditions. In addition, predicted strength according to the analysis results were compared with those by the current design equations, and the equations proposed by previous researchers. As a result, the design formula by the current design equations, such as Korea Building Code (KBC)/American Institute of Steel Construction (AISC) and European Code (EC3), and the equations proposed by Oosterhof and Driver underestimated the base metal block shear strength of ferritic stainless steel by up to 42%. Equations suggested by Topkaya and Lee et al. for carbon steel and austenitic stainless steel welded connections provided more accurate strength predictions, while they did not reflect the difference of material properties. Therefore, this study proposed a modified strength equation for ferritic stainless steel welded connection with base metal block shear fracture considering the stress triaxiality effect of the welded connection and the material properties of ferritic stainless steel. [ABSTRACT FROM AUTHOR]

In this paper, the block shear fracture behavior of base metal in austenitic stainless steel (STS304, corresponds to ASTM 304 type) fillet-welded connection has been investigated through experimental and numerical methods. Even though the block shear fracture strength of welded connection thanks to stress triaxiality effect differs from those of bolted connection under monotonic tension, block shear strength equations of welded connection with base metal fracture in the design codes are identical to those of bolted connection. Main variables are weld method (TIG and Arc welding) and weld length (transverse and longitudinal to the direction of loading). It is found from study results that welding method did not affect the strength of welded connection. Block shear strengths by current codes (KBC2016, AISC2016 and EC3 1–3) and other researchers' proposed equations were compared with those of experimental results and finite element analysis results. Finite element analysis (FEA) model was developed based on previously test data. Also, parametric study for investigating the weld length effect on strength has been performed with the developed finite element analysis procedures. Consequently, condition of weld length and end distance perpendicular to the direction of applied force for fracture mode transition boundary from tensile fracture to block shear fracture in welded connection was investigated. In addition, block shear strength equation with modified tensile stress and shear stress factors of base metal fracture in austenitic stainless steel (STS304) welded connection is suggested considering stress triaxiality. • Finite element analysis of stainless steel welded connections was conducted. • Strength and fracture mode by analysis agreed with those of test results. • Specimens failed by block shear fracture of base metal. • Condition of fracture transition according to variables were investigated. • Effective tensile and shear stress factors were suggested. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of High Pressure Physics is the property of Chinese Journal of High Pressure Physics Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• Water-cooling reduces ductility and increases tensile strength due to formation of martensite phase. • Air-cooling results in a slight increase in ductility and reduction in tensile strength. • High stress triaxiality combined with water-cooling results in significant loss of ductility. The goal of this paper is to understand the post-fire mechanical behavior of ASTM A572 Gr. 50 structural steels cooled from high temperatures using both air-cooling (slow cooling rate) and water-cooling (rapid cooling rate) methods under the influence of high stress triaxiality. In this study, various levels of stress triaxialities in uniaxial tension specimens are achieved by introducing notches in the test specimens. The uniaxial notched test specimens are subjected to temperatures ranging between 500 °C and 1000 °C at 100 °C intervals to simulate fire temperatures. The furnace-heated specimens are then either left outside the furnace for air-cooling or quenched in a water bath in the case of water-cooling method. Uniaxial tension tests are performed on both air and water cooled notched specimens to extract the post-fire mechanical properties. Non-linear finite element analyses are performed to obtain the triaxiality profiles along the critical cross sections of notched specimens by employing hardening curves obtained from post-fire uniaxial tension tests. Moreover, microstructures at selected temperatures are obtained to assess the microstructural changes that caused a significant change in post-fire mechanical properties. It is observed that ASTM A572 steels do no exhibit considerable change in mechanical properties when exposed to temperatures up to 600 °C, for both cooling methods. Beyond 600 °C, air-cooling resulted in a reduction in yield strength and ultimate tensile strength and increase in ductility of ASTM A572 steels. Water-cooling from temperatures beyond 600 °C increased the ultimate tensile strength and decreased the ductility of ASTM A572 steels due to the formation of the martensite phase. High stress triaxiality leads to the reduction in ductility and an increase in yield strength and ultimate tensile strength of ASTM A572 steels in both air-cooled and water-cooled conditions. The combined influence of high stress triaxiality and formation of martensite phase resulted in significant increase of up to 158% in yield strength and up to 172% increase in ultimate tensile strength of ASTM A572 steels that are water-cooled after exposure to temperatures beyond 800 °C. On the other hand, the presence of the high stress triaxiality and water-cooling resulted in up to 89% loss of ductility of ASTM A572 steels specimens that are exposed to temperatures beyond 800 °C. [ABSTRACT FROM AUTHOR]

In addition to the stress triaxiality, the Lode angle has recently been recognized as an important parameter influencing the ductile crack initiation, propagation and final failure of structural steels. In this paper, a modified ductile fracture model is proposed to consider the effects of different stress states on the ductile fracture behavior of steels by introducing the deviatoric state parameter. Different stress states, including the tension, compression, shear, tension-shear, and compression-shear states, can be expressed by the stress triaxiality and deviatoric state parameter relating to the Lode angle. Three flat bar tension specimens and eight flat bar shear specimens were designed to model the different stress states, and ductile fracture tests were carried out on these 11 specimens. The parameters of the modified ductile fracture model in this study were determined based on these ductile fracture tests, and the corresponding finite element analytical results regarding these specimens exhibited strong agreement with the tested results. The proposed model was verified as being suitable for simulating the ductile fracture behavior of steels under different stress states. • A modified ductile fracture model including effect of Lode angle is proposed. • Eight shear specimens were tested to simulate compression-shear and tension-shear stress states. • Different stress states can lead to different ductile fracture behavior of steels. • Six material parameters in the proposed model were determined for SM490 steel. [ABSTRACT FROM AUTHOR]

The initiation of ductile fracture in grade DH36 shipbuilding steel was modeled using the Hosford-Coulomb fracture model. The hardening and ductile fracture characteristics of DH36 were assessed by performing experiments on notched tension, central hole tension, plane strain tension and shear specimens. Detailed finite element analysis of each experiment was performed to evaluate the evolution of local stress and strain fields. The loading paths to ductile fracture initiation were determined in terms of the stress triaxiality and Lode angle parameter histories extracted from finite element analyses with very fine solid element meshes. The Hosford-Coulomb fracture model parameters were identified using the extracted loading paths and adopting a linear damage accumulation law. It has been found that ductile fracture behavior of DH36 is dependent not only on the stress triaxiality but also the Lode angle. • Material specific fracture initiation model for DH36 is presented. • Ductile fracture of DH36 grade steel is sensitive to both stress triaxiality and the Lode angle. • Hosford-Coulomb fracture model is suitable for predicting the fracture initiation in grade DH36 steel. • Increased hardening rate and yield strength decreases Lode angle sensitivity and ductility. [ABSTRACT FROM AUTHOR]

Micromechanics-based models provide powerful tools to predict initiation of ductile fracture in steels. A new criterion is presented herein to study the process of ductile fracture when the effects of both stress triaxiality and shear stress on void growth and coalescence are considered. Finite-element analyses of two different kinds of steel, viz. ASTM A992 and AISI 1045, were carried out to monitor the history of stress and strain states and study the methodology for determining fracture initiation. Both the new model and void growth model (VGM) were calibrated for both kinds of steel and their accuracy for predicting fracture initiation evaluated. The results indicated that both models offer good accuracy for predicting fracture of A992 steel. However, use of the VGM leads to a significant deviation for 1045 steel, while the new model presents good performance for predicting fracture over a wide range of stress triaxiality while capturing the effect of shear stress on fracture initiation. [ABSTRACT FROM AUTHOR]

Abstract Due to the texture formed in cold/hot rolled forming process, anisotropy is a key issue not only in modeling of plastic deformation but also in characterization of fracture behavior. In this study, an anisotropic ductile fracture criterion is developed by introducing anisotropic parameters into the weight function of an uncoupled shear ductile fracture criterion. The proposed anisotropic ductile fracture is applied to describe the anisotropic characteristics in the ductile fracture of AA6082-T6. Ductile fracture behavior of AA6082 is experimentally investigated at the different loading conditions: shear by in-plane torsion test, uniaxial tension by specimens with a central hole, plane strain tension by notched specimens, and the balanced biaxial tension by the Nakajima test. In-plane torsion and tension tests with a central hole and notch are conducted along three directions: rolling direction, diagonal direction and transverse direction. Specimen deformations during the tests are recorded and fracture strains are measured by digital image correlation approach. The measured fracture strains are then utilized to calibrate the parameters in the proposed ductile fracture criterion. With the calibrated ductile fracture criterion, the fracture locus and anisotropic ductile fracture in various loading conditions are predicted and compared with experimental measurement and those predicted by linearly transformed anisotropic fracture model to investigate the predictability of the proposed ductile fracture criterion. The comparison demonstrates that the anisotropic fracture of AA6082 is predicted by the proposed criterion with good agreement in the different loading directions of shear, uniaxial tension, plane strain tension, and the balanced biaxial tension. Considering the high accuracy of the proposed ductile fracture criterion, it is expected that the proposed anisotropic ductile fracture criterion can improve the reliability of failure prediction in metal forming for materials with strong directionality in fracture. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Acquiring a full range of yield curves is a long-standing challenge in material science and engineering. Such curves are extremely important for stress analysis using finite element simulation. In this article, we proposed an improved procedure integrating finite element analysis and hybrid particle swarm optimization to extract a post-necking yield curve from a smooth tensile round bar. The investigated material was 3Cr1MoV. The strain range of the yield curve was extended from 0.0681 mm/mm before necking to 1.5 mm/mm. The results revealed that curves obtained through this procedure are reliable and unique. Three notched round bars were designed to investigate the effects of stress triaxiality on the yield curves. We found that stress triaxiality has a significant influence on curves at large plastic strains (strain > 0.3 mm/mm) and has a negligible effect at low plastic strains (strain < 0.3 mm/mm). Studies revealed that the stress triaxiality-dependent yield curves are related to dilatational plasticity arising from nucleation and growth of voids. [ABSTRACT FROM AUTHOR]

• Present different J and K along crack fronts in CCT and CT specimens. • Present different near-tip stresses in CCT and CT specimens. • Determine lower fracture initiation load for CCT than those for CT and PT specimens. • Visualize localized plastic strain between circumferential hydrides in CCT specimens. • Show similar percentage of fracture toughness reduction for all hydrided specimens. The effects of curvature on K, J, plastic zone, near-tip stress and fracture initiation in curved compact tension (CCT) specimens of unhydrided and hydrided irradiated Zr-2.5Nb materials are determined by three-dimensional finite element analyses. Based on a strain-based failure criterion, the fracture initiation load for unhydrided CCT specimens is slightly lower than those for unhydrided compact tension (CT) and pressure tube (PT) specimens. For hydrided specimens, the reductions of fracture initiation loads for CT, CCT and PT specimens are similar. The fractions of fracture initiation loads for hydrided specimens are about 60–70% of those for unhydrided specimens. [ABSTRACT FROM AUTHOR]

A new constitutive model σ eq = 1 - D ‾ f η 〈 l n p - ln p th 〉 ln ε f - ln p th σ y (p) 1 - η - η 0 f η 0.5 1 + α η - η 0 ln p ̇ p ̇ 0 to predict fracture initiation sites, and decay of fracture strain. • Evaluation of a new stress triaxiality-dependent viscoplastic damage model for ductile fracture. • Transferability of model parameters over a large range of positive stress triaxialities. • Consistency viscoplastic regularization method for mesh independency and strain softening. • Prediction for decay of fracture strains and transition of fracture initiation locations in notched tensile specimens. The aim of this paper is to gain insight for the transition of fracture initiation sites in notched tensile specimens. For this purpose, a stress triaxiality-dependent viscoplastic damage model was proposed for various types of notched tensile specimens, where the influence of stress triaxiality on damage, damage-free stress-strain curve and viscoplasticity was considered. Also, in this constitutive model, the consistency viscoplastic regularization method was used to solve the pathological mesh-dependent problem due to strain softening. A hybrid experimental-numerical approach was used to calibrate model parameters by using smooth and one type of round-notched tensile specimens. The same set of model parameters was then applied to predict ductile fracture for three other types of round-notched tensile specimens. Good agreement between experimental data and simulation results confirmed the transferability of model parameters to all types of tensile specimens considered and the ability of the proposed constitutive model to predict ductile fracture over a large range of positive stress triaxialities. This study found that at the onset of fracture critical damage parameters for all five types of tensile specimens were relatively constant, and fracture initiation sites in these specimens were associated with critical damage parameters, shifting from the center to the notch root. Therefore, the critical damage parameter was defined as a ductile fracture criterion and the fracture strain for all the five types of tensile specimens was successfully predicted. [ABSTRACT FROM AUTHOR]

Abstract In this work, the yielding response of high-density polyethylene (HDPE) under different stress states and strain rates was experimentally examined and the ability of classical yield criteria to capture their deformation response assessed. A series of biaxial loading tests (pure shear, combined shear and tension/compression, pure tension/compression) using a designed Arcan testing apparatus were performed. In order to investigate a wider range of stress states, flat and cylindrical notched specimens with different curvature radii were also tested. The predictive ability of the Von Mises and the Drucker-Prager yield criteria are compared against the acquired experimental data. The Drucker-Prager yield model allowed an improved description of the available experimental results, demonstrating the need to account for pressure dependency in the yield model's formulation for semi crystalline polymers. Some differences observed may be attributed to the third invariant stress tensor effects. The evolution of stress triaxiality and Lode angle parameters with equivalent plastic strain were extracted from simulations with Drucker-Prager yield criterion. The results show sensitive stress state dependency of the plastic yielding behaviour, which can be attributed to different combinations of stress triaxiality and Lode angle parameters. Also numerical simulations show that there is variation of the stress triaxiality and equivalent plastic strain along the cross section and the location of the maximum plastic strain and maximum stress triaxiality in the specimens are located at the centre of the specimens. [ABSTRACT FROM AUTHOR]

Highlights • Proposed mini-Nakazima fracture experiment with dihedral punch. • Observed proportional loading path until fracture initiation. • Compared results with notched tension and V-bending. • Validated for aluminum 2024-T351, DP450, DP980. Abstract A new experimental technique is proposed for measuring the strain to fracture for sheet metal after proportional loading under plane strain conditions. The proposed technique makes use of a mini-Nakazima specimen that is clamped onto a 30 mm diameter die and subjected to out-of-plane loading through a dihedral punch. While other techniques for determining the strain to fracture for plane strain tension loading (e.g. notched tension or V-bending) suffer from limitations with regards to the thickness and ductility of the material to be characterized, the mini-Nakazima experiments are more robust and universally applicable. Experiments are performed on mini-Nakazima, notched tension and V-bending specimens extracted from 1.2 mm thick aluminum 2024-T351, 0.8 mm thick DP450 and 1.6 mm thick DP980 steel. In addition, detailed numerical simulations are performed for each experiment. The hybrid experimental-numerical results show the limitations of existing experimental techniques and demonstrate the reliability of the proposed stretch-bending technique. As a by-product, it is shown that the Yld2000-3D yield function with associated flow rule provides a reasonably accurate description of the large deformation response of aluminum 2024-T351. Equally good predictions are obtained for the DP450 and DP980 steels when using a von Mises yield function in conjunction with a non-associated Hill'48 flow rule. Furthermore, to characterize the effects of the stress triaxiality and the Lode angle parameter on the fracture response of the above materials, the strains to fracture are determined for simple shear and equi-biaxial tension. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

To meet requirements for reduced fuel consumption of cars, the use of components made of sheets of high-strength steel instead of conventional steel has been on the rise. However, low ultimate elongation of high-strength steel often causes problems during plastic deformation and more research is needed to improve failure predictability. Ductile failure models available in commercial finite element analysis (FEA) packages require the material's tensile strength and failure strain for failure prediction. For stress states that are more complex than the uniaxial case, accurate prediction of the how, when, and where failure occurs has been become problematic and it has been investigated by numerous researchers. In this study, we investigate the prediction of failure in DP980 sheets under triaxle stress states. We first determine the shapes of specimens using certain triaxial stress states, such as pure shear, uniaxial tension, biaxial deformation, which are induced by corresponding tensile tests. When failure occurs, equivalent strain at the failure locus is obtained by means of digital image correlation (DIC) and then plotted against triaxiality and Lode angle, based on which the triaxiality failure diagram (TFD) is established to implement in the FEA program of LS-DYNA. Validation is made by comparing the numerical results with burring test data. Good agreement was found for failure locus and strain distribution at the time of failure. [ABSTRACT FROM AUTHOR]

Abstract The response surface methodology in the design of experiments (DOE) wizard and Gurson-Tvergaard-Needleman (GTN) model were employed to estimate the optimum GTN damage parameters and to validate their significant effects respectively on the ductile fracture behavior of ECAP deformed AZ61 magnesium alloy. Hollomon's flow stress was applied to identify uniform deformation and non-uniform deformation regions to investigate the void nucleation and coalescence processes separately. The significance of statistical results was evaluated with the analysis of variance (ANOVA) based on P-values and coefficients of determination (R 2). Correspondingly, the contributions of ECAP plastic deformation and the corresponding local plasticity (damage progresses) on the progress of GTN ductile fracture damage parameters were studied. Desirability function was used to show the significance of individual and interaction effects of optimum initial damage parameters on the respective response variables. By using response surface methodology, the optimum GTN damage parameters were determined at the corresponding positions of each critical response variables. Results also showed that varying both stress triaxiality and damage variables simultaneously can greatly affect the curve fitting process of experimental, simulation and GTN model curves. However, at constant stress triaxiality condition, the GTN model curve was observed perfectly fitting with the tensile test curve. [ABSTRACT FROM AUTHOR]

Highlights • A continuum damage mechanics (CDM) and XFEM based methodology is developed for high cycle fatigue crack growth simulations. • A new damage model is proposed for the evaluation of fatigue crack growth life. • A new criterion is proposed based on the damage evolution to identify the appropriate definition of stress triaxiality. • A non-local CDM approach is implemented to reduce the mesh sensitivity. • The present methodology is found quite successful for fatigue crack growth simulations. Abstract In this paper, we have developed a continuum damage mechanics (CDM) based methodology for high cycle fatigue crack growth simulations. A fatigue damage law is proposed and implemented in the framework of extended finite element method (XFEM). A new criterion is proposed based on damage evolution to identify the appropriate definition of stress triaxiality for acquiring the constraint effect on the stress state correctly. Few mesh regularization schemes are also employed for reducing the mesh sensitivity in the results. Simulations are performed on fracture specimens of different materials subjected to constant amplitude fatigue loading. The fatigue life of a turbine disc is also predicted under constant amplitude loading. The results obtained from present methodology (CDM and XFEM) are found in good agreement with the published experimental results. These simulations highlight that the continuum damage mechanics is a simple and effective tool to perform crack growth simulations under high cycle fatigue conditions. [ABSTRACT FROM AUTHOR]

Highlights • The influence of stress triaxiality on the material formability in SPIF tests is discussed and compared with conventional Nakajima tests in the ɛ ¯ − η ¯ space. • The analytical procedure of mapping the FFL from the ε 1 − ε 2 space to the ɛ ¯ − η ¯ space, using the kinked strain path associated to the onset of local necking in Nakajima tests, is presented. • The difference in the average stress triaxiality at fracture exhibited in SPIF and Nakajima tests would allow explaining the enhancement on formability observed in incremental sheet forming. Abstract Traditionally the fracture in sheet metal forming is characterized by the fracture forming limit (FFL) curve typically obtained by using conventional Nakajima tests. This curve is implicitly assumed a material property. Single point incremental forming (SPIF) is a novel and flexible forming process characterized by the ability to suppress local necking and develop stable plastic deformation up to sheet fracture. In many cases, these fracture strains are clearly above the conventional FFL. The current work presents a numerical study of the evolution of stress triaxiality in SPIF in the ɛ ¯ − η ¯ space. The simulations are validated with hole-flanging tests by single-stage SPIF over AA7075-O sheet of 1.6 mm thickness. The difference in the average stress triaxiality at fracture exhibited in SPIF and Nakajima tests would allow explaining the enhancement on formability observed in incremental sheet forming. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

The block shear equations specified in the current AISC specification for structural steel buildings and North American cold-formed steel design specifications are based on research results of carbon steel bolted connections. These equations were found to be inapplicable for the welded connections in the literature. This issue is primarily associated with the use of the incorrect assumption on block shear failure mechanism. The present paper examines the accuracy of various block shear equations available in the design specifications and in the literature. The paper also examines the shear hardening capacity and the level of tensile stress over the critical net area with the results of finite element analysis, in which the fracture simulation is considered. It shows that the block shear capacities of lean duplex stainless steel welded connections can be predicted accurately using tensile stress equal to 1.25Fu, as proposed in the literature.

In contrast to other cutting processes, adiabatic blanking typically features high blanking velocities (>3 m/s), which can lead to the formation of adiabatic shear bands in the blanking surface. The produced surfaces have excellent properties, such as high hardness, low roll-over, and low roughness. However, details about the qualitative and quantitative influence of significant process parameters on the quality of the blanked surface are still lacking. In the presented study, a variable tool is used for a systematic investigation of different process parameters and their influences on the blanked surface of a hardened 22MnB5 steel. Different relative clearances (1.67% to 16.67%), velocities (7 to 12.5 m/s), and impact energies (250 J to 1000 J) were studied in detail. It is demonstrated that a relative clearance of ≤6.67% and an impact velocity of ≥7 m/s lead to adiabatic shear band formation, regardless of the impact energy. Further, an initiated shear band results in the formation of an S-shaped surface. Unexpectedly, a low impact energy results in the highest geometric accuracy. The influence of the clearance, the velocity, and the impact energy on the evolution of adiabatic shear band formation is shown for the first time. The gained knowledge can enable a functionalization of the blanked surfaces in the future.

In this paper, the stress corrosion and monotonic tensile test of corroded steel wire were carried out. The effects of different corrosion ages and stress levels on failure modes, stress-strain curve and mechanical properties of corroded steel wire were discussed. Then, a finite element model of steel wire considering real surface morphology was established, and the surface stress distribution and the failure of steel wire under different corrosion degrees were compared. The relationship between stress triaxiality and critical equivalent plastic strain to different corrosion parameters was given. Finally, the degradation model of mechanical properties of corroded steel wires was established. The results showed that the failure patterns of steel wires with different degrees of corrosion were mainly divided into three types: cup cone shape, milling cutter shape and splitting shape. The shear lip zone of fracture section basically disappeared with the increase of stress corrosion, and the location of fiber area was transferred from the inside to the surface of steel wire. The decrease in strength and elastic modulus of the specimen under stress corrosion was four times and three times greater than that under non-stress corrosion, respectively. In addition, the crack position of specimen changed from the inside of section to the location of corrosion pit with the increase of corrosion degree. The fracture equivalent plastic strain decreased gradually, while the stress triaxiality increased. When the degree of corrosion reached 19.53%, the fracture equivalent plastic strain decreased by 55.41% from 0.314 to 0.140, and the stress triaxiality increased by 23.53% from 0.390 to 0.510. The influence of uniform thickness loss on the stress triaxiality was less than that of pit depth-width ratio. The larger the depth-width ratio, the larger the maximum stress triaxiality corresponding to the failure element. The constitutive model proposed in this paper could reflect the degradation law of mechanical properties of corroded steel wires. • The effect of corrosion ages and stress levels on the mechanical properties of corroded steel wire was discussed. • The stress distribution and failure of steel wire under different corrosion degrees were compared. • The degradation model of mechanical properties of corroded steel wires was established. [ABSTRACT FROM AUTHOR]

• The new tensile tests combining with finite element simulations were developed. • Weakening during post-necking deformation was firstly found in 1.5-GPa class steel. • Weakening behavior did not follow the previously developed damage models. • X-ray diffraction analyses detected material damage relating the weakening. • Unobservable vacancies are likely responsible for damage resulting in weakening. The weakening behavior of ultra-high-strength steel(UHSS) remains unknown, even though it is a requirement for the accurate prediction of strain localization and ductile fracture in automobile applications. In this study, we, therefore, revealed the stress–strain curves of UHSSs up to their ductile fracture under different stress triaxialities for the first time. Smooth and notched tiny round-bar specimens cut from UHSSs with 1.6 mm thickness were subjected to tensile tests, during which the forces and neck diameters of the specimens were measured. Notably, the evaluated flow stresses in the 1.5 GPa-class notched UHSS specimens exhibited weakening of up to 3%. This was in contrast to the 980 MPa-class UHSS specimens, which did not exhibit notch-induced weakening. The absence of weakening during stress measurements, as confirmed by synchrotron X-ray diffraction (XRD) analysis, suggested that weakening was caused by material damage. However, the weakening behavior did not follow the previously developed damage models based on microvoid formation. The volume fraction of the microvoids, as observed by X-ray computer tomography, was extremely small (at 0.2%) and cannot account for the 3% material weakening indicated by the flow stress measurement results. A new damage mechanism, associated with unobservable small lattice vacancies, was implied in UHSSs deformation under high stress triaxialities. [Display omitted] [ABSTRACT FROM AUTHOR]

The impact of high stress triaxiality on work hardening in transformation-induced plasticity (TRIP) steel has been widely acknowledged, particularly through measurements of the austenite fraction. Understanding this TRIP behavior is crucial for predicting material fracture in press-forming processes. However, the actual flow stresses under high-stress-triaxiality conditions remain largely undetermined. To address this gap, we developed a new tensile testing method using tiny notched round bars to investigate stress-triaxiality-induced work hardening in TRIP steels. The specimens were analyzed using two-dimensional micrometry to allow finite element analyses to identify the flow stress. Additionally, we conducted in situ tensile tests in which their crystal lattice stresses were monitored using synchrotron X-ray diffraction (XRD) to realize mechanism analyses of the unexpected work-hardening behavior identified by the developed tensile testing method. Our combined approach revealed a mutual, unstable increase in the flow stress and stress triaxiality in the TRIP-aided bainitic ferrite steel, which reduced the hardening exponent coefficients and thus induced a higher stress triaxiality. In contrast, the TRIP-aided martensitic steel exhibited a weakening behavior, characterized by a significant decrease in the hardening exponent coefficients in the case of the sharpest notch. XRD analyses showed that microstructural heterogeneity led to an extraordinarily high hydrostatic stress in the austenite phase, accounting for these contrasting behaviors. This finding challenges the established consensus on TRIP steels and suggests the need for a revised framework for their application in press-forming, taking into account stress-triaxiality conditions. [Display omitted] • New tensile testing method using tiny notched round bars was developed. • Stress-triaxiality-induced hardening (STH) was directly evaluated in TRIP steels. • Instable stress triaxiality increase by STH was newly discovered. • Weakening behavior instead of STH was firstly found in high strength TRIP steel. • Extremely high hydrostatic stresses on the austenite phase caused weakening. [ABSTRACT FROM AUTHOR]

• A generalized plasticity framework for tension‒compression asymmetry (TCA) was developed. • The new framework was applied to various yield functions: Hill48, Yld2k-2d, Poly6, and Min2016. • Accurate TCA capture was achieved in plastic anisotropy under uniaxial and equi-biaxial loads. • Anisotropy-asymmetry in dual-phase steel, Al, and Ti alloys was successful predicted. • The new framework reproduced anisotropic hardening in Q&P steel using analytical calibration. Microstructural characteristics and complex loading conditions in the deformation of metallic materials lead to complexity in mechanical responses. In this study, we propose a generalized constitutive framework that reproduces the plastic anisotropy and asymmetry under various loading conditions. Particularly, the developed model can accurately capture distinctive flow stress, plastic flow and strain hardening between tensile and compressive dominant loadings under a wide range of stress states. The model is based on the stress triaxiality dependence of state variable (or weighting factor) newly incorporated in the existing plasticity theory to keep the computational efficiency and versatility. For example, the new generalized framework can be applied to widely employed Hill48, Yld2k-2d, and Poly6 as a class of associated flow rule-based yield functions, as well as Stoughton-Yoon2009 and Min2016 yield functions for the non-associated flow rule. Also, the model is adaptable when selecting the yield function under tension or compression, which efficiently controls the degree of accuracy in anisotropic modeling under tension and compression. The generalized plasticity framework is validated comprehensively by demonstrating the predictive capability for anisotropy in yield stress and plastic flow of metallic materials with different crystal structures. Moreover, the model can efficiently capture the continuous evolution of asymmetric yield surfaces as functions of strain, temperature, and strain rate. Finally, the identification procedure of the model is discussed by demonstrating the analytical determination of model parameters utilizing the experimental or generic material data obtained from various loading conditions such as tension, compression, plane strain loading, and pure shear. [ABSTRACT FROM AUTHOR]

• Post-fire tension tests were performed on Q690 steel under plane strain state. • Post-fire tension tests were performed on Q690 steel under generalized tension state. • Post-fire stress state-dependent strain to fracture surface for Q690 steel was obtained. • Stress states influence post-fire ultimate strength of Q690 steel. Fire is one of the most dangerous disasters for high-strength steel structures. After a fire event, the deterioration of mechanical properties of high-strength steel together with the complex stress state generated by external loading may lead to an unexpected failure or collapse of high-strength steel structures. Therefore, it is very critical to evaluate the post-fire behavior of high-strength steel considering stress state effects. This study conducted a series of tests on the Q690 steel specimens after being exposed to high temperatures ranging from 200 to 1000°C with different cooling methods including air-cooling and water-cooling methods. The tested specimens including smooth round specimens, notched round specimens, and grooved plate specimens were designed to consider the failure mode in axisymmetric stress state and plane strain state. To validate the accuracy of the test results, the mechanical properties such as yield strength, ultimate strength, elastic modulus, and ultimate strain were first compared with other test results reported in the literature. The post-fire ultimate strength under different stress states was obtained directly from the test results. Then, the post-fire equivalent plastic strain at fracture of different specimens was obtained from test data together with the finite element analysis results and analyzed under different stress triaxialities and Lode angle parameters. According to this study, an increase in stress triaxiality can result in an increase in ultimate strength but a decrease in the equivalent plastic strain at fracture for Q690 steel after fire. When the exposed temperature was not higher than 800°C, the post-fire strength of the plane strain specimen (Grooved Plane Specimen) was higher than that of the axisymmetric tension specimen (Notched Round Specimen) under a similar stress triaxiality; however, for their post-fire equivalent plastic strain at fracture, the results were opposite. [ABSTRACT FROM AUTHOR]

One of the main concerns of pipeline design engineers for ultra-deepwater applications is to predict the pipes' collapse capacity due to buckling caused by the hydrostatic pressure. DNV-ST-F101 is one of the most used guides for such systems, and presents the equations for the computation of the collapse pressure of submarine pipelines considering a limited diameter-to-thickness (D / t) range, not taking into account thick-walled structures. This work aims to investigate the accuracy of DNV-ST-F101 equations for submarine pipes with low D / t ratios. We show that, for these specific configurations, the analytical equations provided tend to underestimate the collapse capacity, which might result in the design of unnecessarily thick structures. Using finite element analyses we conclude that thick-walled pipes show a high level of stress triaxiality inside its wall at the moment of collapse, making it necessary a different analytical approach than that of DNV-ST-F101. Finite element simulations of four different metallic materials and five pipe configurations (D / t ratios) are performed to develop an alternative approach for the computation of the plastic collapse of pipes under hidrostatic pressure that takes into account the stress triaxiality at the moment of the pipes' collapse. Our results improve the accuracy of the original DNV design equation for pipe diameter-to-thickness ratio within the range commonly found in the pre-salt offshore exploration. • Finite element simulation of thick-walled pipes. • Computation of stress triaxiality inside the pipes' wall. • Novel equations for the collapse pressure of pipes. • Good results for thick- and thin-walled pipes. [ABSTRACT FROM AUTHOR]

[Display omitted] • Tracking the void nucleation and growth of dual phase steel by Computed Tomography. • New voids were observed to nucleate throughout the straining process. • The average size of void grows only slowly with straining. • New damage model is proposed for void nucleation and growth in dual phase steel. In situ synchrotron radiation X-ray computed tomography (CT) is used to understand the void nucleation and growth behaviour of dual phase (DP) steel, DP800, during uniaxial tensile deformation. The voids were identified post mortem as having nucleated primarily in the (41 vol%) martensite phase. The behaviour of individual voids was found to be broadly in line with a Rice and Tracey style growth model (their volume increasing by a factor of 10), while the mean void size was broadly in line with a model that included the continuous nucleation of new voids, as well as the growth of existing voids, throughout straining. Voids tended to elongate during uniaxial (low stress triaxiality) straining, but then to dilate more isotropically as necking led to increased triaxiality. One large pre-existing void was found to elongate quicky at first, but then for growth to slow, presumably because it was not located in the highest triaxial stress (necked) region. Perhaps surprisingly the average size of the void population grows only slowly (by a factor of 2) during straining; this is because while the size of each void grows, new small voids are always being nucleated. Finally, the changes of stress triaxiality and shear stress state during tensile deformation of the square cross-section smooth tensile specimen are investigated via finite element modelling, to qualitatively assess the impact of sample geometry on void nucleation behaviour and fracture strain in the current study. [ABSTRACT FROM AUTHOR]

[Display omitted] • The ductile fracture of LYP225 steel has been investigated. • The stress state and loading history dependencies are considered. • The stress state dependency can be described by Hosford-Coulomb fracture model. • A generalized form of cut-off region is proposed. • A reduction factor is proposed for the damage accumulation rate under cyclic loading. This paper presents the experimental and modeling studies of the ductile fracture initiation of LYP225 steel, considering the stress state and loading history dependency. The monotonic material tests, including the notched round bars (NRBs), flat grooved plates (FGPs), and the shear plates (SPs), confirm the prominent stress state dependency of the ductile fracture. The increased stress triaxiality will significantly reduce the fracture strain, and the shear effect quantified by the Lode angle parameter will degrade the deformability under similar triaxiality. The Hosford-Coulomb fracture criterion can well characterize the relationship between fracture strain and stress state variables. Regarding the cyclic loading, a generalized expression of the cut-off region is proposed to consider the temporarily frozen damage accumulation under compression applied. In addition, the premature cyclic fracture initiation predicted by the monotonic fracture criterion highlights the necessity of considering the loading history effect. Based on the plastic strain memory surface, a reduced factor is introduced for the lower damage accumulation rate under cyclic loading. By comparing the testing and predicted plastic deformation corresponding to fracture initiation, the proposed fracture model is validated under different stress states and loading protocols, as indicated by the low average percentage errors of 4.02% for monotonic loading and 16.7% for cyclic loading. [ABSTRACT FROM AUTHOR]

Bolt fracture often limits the ultimate strength and deformation capacity of bolted connections and leads to overall joint failure. Therefore, the prediction of structural collapse under extreme loads necessitates the incorporation of a reliable fracture model that reflects the observed structural response of bolts. This paper reports a comprehensive experimental and numerical study into the structural behaviour, ductility and fracture characteristics of Grade A4–80 austenitic stainless steel bolts and carbon steel 8.8 bolts in tension, which are commonly used as fasteners in bolted connections. Tensile tests were performed on smooth material coupons machined from both bolt grades to obtain the material response. Thereafter, tensile tests were performed on notched specimens from both grades, allowing the fracture characteristics to be studied over a range of stress triaxialities and the development of an equation relating the plastic strain at fracture to the stress triaxiality. 2D axisymmetric and 3D advanced finite element models were calibrated against the experimental results and damage propagation parameters. The developed numerical models are shown to perfectly replicate the observed experimental behaviour of the tested bolt materials under predominantly tensile loading, including fracture. Both experimental and numerical results confirm the superior ductility of A4–80 bolts over their 8.8 counterparts. • Experimental tests on carbon steel and stainless steel bolt material with various stress triaxialities were conducted. • An equation relating equivalent plastic strain at fracture to the stress triaxiality was proposed. • 2D axisymmetric and 3D advanced finite element models were developed and calibrated against the experimental results. • FEmodels accurately captured the ultimate response and the fracture of 8.8 carbon steel and A4–80 stainless steel bolts. • Superior ductility of A4–80 stainless steel bolts over their 8.8 carbon steel counterparts was revealed. [ABSTRACT FROM AUTHOR]

In this work, the ballistic response of an armor steel, Armox 500T, is numerically investigated through finite element (FE) analysis by utilizing the Johnson–Cook (JC) and modified Mohr–Coulomb (MMC) damage models, with a focus on emphasizing the consequences of different modeling approaches. Although Lode-dependent failure models are considered to increase the accuracy of numerical predictions for ductile failure, there remains a complete lack of clarity as to whether all conditions and materials necessitate the adoption of such models for ballistic impact simulations. In this context, MMC and JC model parameters are calibrated through tensile test data available in the literature enabling direct comparison between them. Damage models are then validated using ballistic impact tests of Armox 500T performed with 7.62 API projectiles. The results indicate that the MMC model outperforms the JC model at predicting the failure modes while both models demonstrate strong performance in anticipating the residual velocity. The influence of projectile nose shape, target plate thickness, and impact angle are further investigated, and the effect of incorporating the Lode parameter is discussed in detail. Impact simulations with the blunt projectile nose shape is found to be highly sensitive to the effect of Lode angle on failure, with differences of up to 20% between models, while 7.62 API shows the lowest sensitivity. The difference between the models' predictions is observed to increase at lower impact velocities and higher impact angles demonstrating the necessity of a Lode-dependent failure model for such cases. The JC model consistently yields smaller residual velocities compared to the MMC model in all cases indicating that the MMC is more conservative in terms of predicting protective performance of Armox 500T. • JC and modified MMC damage model parameters are calibrated for armor steel Armox 500T. • The effect of Lode-dependent failure is studied for various impact scenarios. • At higher velocities, failure is dominated by strain rate effects rather than the stress state. • Failure with blunt projectiles is found to be highly sensitive to the Lode parameter. • The MMC model provides more accurate predictions of the ballistic failure mode compared to the JC model. [ABSTRACT FROM AUTHOR]

Forty-eight specimens with four notch specimen configurations have been extracted from three structural steel grades used in the Indian construction industry. The extracted specimen simulates stress states of ductile fracture initiation similar to the sacrificial element installed in seismic-resistant steel structures. All the specimens are monotonically tested under a displacement-controlled loading protocol. With the help of a universal testing machine and digital image correlation, the load versus notch elongation until the point of ductile fracture initiation has been captured for all the specimens. A validated numerical model is then developed to extract the ductile fracture initiation parameters, namely stress Triaxiality (T), Lode function (L - ξ or θ or L p), and Equivalent Plastic Strain (PEEQ). The extracted T, L, and PEEQ are then used to construct a three-dimensional fracture locus for all three study grades. In addition, a new uncoupled ductile fracture model named the Exponential based Lode parameter Void Growth Model (ELVGM) is proposed to predict the point of ductile fracture initiation and is then compared with six well-established existing uncoupled ductile fracture models using eight error measures. The proposed ELVGM with two free parameters is observed to provide better prediction accuracy for both low and high-yield strength steel corresponding to the considered stress states. [Display omitted] • Fracture locus database is created for three Indian steel grades (E250, E350, E450). • Isotropic hardening and free parameters are calibrated using 48 monotonic results. • New model (ELVGM) shows better prediction accuracy compared to six existing models. [ABSTRACT FROM AUTHOR]

This study investigates the strengthening mechanism of water jet (WJ) on the high-entropy alloy CoCrFeNiAlx (x = 0, 0.6, 1). Finite element simulation analysis was conducted to examine the changes in residual stress, surface roughness, and stress triaxiality of high-entropy alloys under different jet velocities and Al contents. Subsequently, an experimental validation of surface roughness was performed using the Al 1 high-entropy alloy. The results reveal that the residual compressive stress and maximum residual compressive stress on the high-entropy alloy's surface increase with the jet velocity, irrespective of the Al content. However, the depth of the maximum residual compressive stress decreases as the Al content increases. At a jet velocity of 280 mm/s, the residual compressive stress on the surface of the Al 1 high-entropy alloy surpasses that of the Al 0.6 high-entropy alloy. Specifically, the residual compressive stress on the surface of the Al 1 high-entropy alloy is approximately 265 MPa, which is significantly higher than the value of 9 MPa for the Al 0.6 high-entropy alloy. When the jet velocity reaches 300 mm/s, the surface residual compressive stress of the high-entropy alloys shows a positive correlation with the Al content. The residual compressive stress on the surface of the Al 1 high-entropy alloy is about 1.89 times and 1.23 times that of the Al 0 and Al 0.6 high-entropy alloys, respectively. As the jet velocity continues to increase to 320 mm/s, the maximum residual compressive stress of the high-entropy alloys follows the order: Al 0.6 > Al 0 > Al 1. The maximum residual compressive stress of the Al 0.6 high-entropy alloy measures approximately 477 MPa, which is approximately 82 MPa higher than that of the Al 0 high-entropy alloy. Subsequently, at a jet velocity of 340 mm/s, the Al 0.6 high-entropy alloy exhibits the highest maximum residual compressive stress, reaching a value of 650 MPa.Additionally, a negative correlation between surface roughness and jet velocity is observed. Moreover, an increase in Al content within the high-entropy alloys significantly reduces surface roughness under the same jet velocity impact. • The strengthening mechanism of water jet (WJ) was investigated. • The mechanism of influence of different element contents on residual stress was revealed. • The influence of different jet parameters on the strengthening mechanism was investigated. [ABSTRACT FROM AUTHOR]

We propose a primary water stress corrosion cracking (PWSCC) initiation model of Alloy 600 that considers the stress triaxiality factor to apply to finite element analysis. We investigated the correlation between stress triaxiality effects and PWSCC growth behavior in cold-worked Alloy 600 stream generator tubes, and identified an additional stress triaxiality factor that can be added to Garud's PWSCC initiation model. By applying the proposed PWSCC initiation model considering the stress triaxiality factor, PWSCC growth simulations based on the macroscopic phenomenological damage mechanics approach were carried out on the PWSCC growth tests of various cold-worked Alloy 600 steam generator tubes and compact tension specimens. As a result, PWSCC growth behavior results from the finite element prediction are in good agreement with the experimental results.

A comparison is made of the ductility limits of one mild (normal) and two high-tensile strength shipbuilding steels with an emphasis on stress state and loading path dependency. To describe the ductile fracture behavior of the considered steels accurately, an alternative form of ductile fracture prediction model is presented and calibrated. The present fracture model combines the normalized Cockcroft–Latham and maximum shear stress criterion, and is dependent on both stress triaxiality and Lode angle parameter. The calibrations indicate that, depending on the hardening characteristics of the steels, ductile fracture behavior differs considerably with stress state. It is demonstrated that the adopted fracture model is able to predict the ductile fracture initiation in various test specimens with good accuracy and is flexible in addressing the observed differences in the ductile fracture behavior of the considered steel grades.

The aim of this study was to calibrate a material model with two fracture criteria that is available in the DEFORM software on DIN 34CrNiMo6. The purpose is to propose a type of simple test that will be sufficient for the determination of damage parameters. The influence of the quantity of mechanical tests on the accuracy of the fracture criterion was explored. This approach was validated using several tests and simulations of damage in a tube and a round bar. These tests are used in engineering applications for their ease of manufacturing and their strong ability to fracture. The prediction of the time and location of the failure was based on the parameters of the relevant damage model. Normalized Cockroft-Latham and Oyane criteria were explored. The validation involved comparing the results of numerical simulation against the test data. The accuracy of prediction of fracture for various stress states using the criteria was evaluated. Both fracture criteria showed good agreement in terms of the fracture locus, but the Oyane criterion proved more suitable for cases covering larger triaxiality ranges.

The present study investigates the effect of stress triaxiality on mechanical behavior and fracture of Ti-5Al-2.5Sn alloy in a practical relevant strain rate range from 0.1 to 1000 s−1. Tensile tests were carried out on flat smoothed and notched specimens using an Instron VHS 40/50-20 servo-hydraulic test machine. High-speed video registration was conducted by Phantom 711 Camera. Strain fields on the specimen gauge area were investigated by the digital image correlation method (DIC). The fracture surface relief was studied using digital microscope Keyence VHX-600D. Stress and strain fields during testing of the Ti-5Al-2.5Sn alloy were analyzed by the numerical simulation method. The evolution of strain fields at the investigated loading condition indicates that large plastic deformation occurs in localization bands. The alloy undergoes fracture governing by damage nucleation, growth, and coalescence in the localized plastic strain bands oriented along the maximum shear stresses. Results confirm that the fracture of near alpha titanium alloys has ductile behavior at strain rates from 0.1 to 1000 s−1, stress triaxiality parameter 0.33 < η < 0.6, and temperature close to 295 K.

The deformation behaviour and fracture mechanisms of high-density polyethylene (HDPE), polypropylene (PP) and polyamide 6 (PA 6) are investigated experimentally under different stress states and at different crosshead speeds of 1, 20 and 200 mm/min. Fracture surface morphologies were investigated in a series of specimens tested at 200 mm/min under combined tension/shear loading at three different loading angles (α = 0°, 30° and 90°) at room temperature (RT) and 50 °C. In addition, the effects of notch profile radii (stress triaxiality) on HDPE, PP and PA 6 fracture behaviour have been studied at RT, using flat and cylindrical notched specimens. Specimens’ geometries were carefully designed to achieve various loading conditions and allowing to explore initial stress triaxialities ranged from 0 in pure shear loading (α = 0°) to a maximum of 0.84 for flat notched specimens with radius of 5 mm. The yield load shows an explicit dependency on temperature and crosshead speed. The fracture surfaces analysed reveals damage mechanisms such as crazing, void and cavitation formation. Two or more mechanisms are predominant, which means that the stresses along fracture process are not uniform.