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Structural steel (E250 grade) is used in several engineering applications involving loadings from quasi-static to high strain rates (blast discs, explosion vents, etc.), which introduce large deformation, strain and strain rate hardening, thermal softening, and damage to the material. The material's dynamic constitutive behaviour can be aptly modelled by a visco-plasticity-based Johnson–Cook (J–C) strength model and damage initiation and complete failure by the J–C's damage model. In the latter, damage initiation is modelled through continuum damage mechanics and propagation by the fracture mechanics. This paper focuses on the determination of 10 different J–C's dynamic constitutive and damage model parameters for E250 structural steel by conducting several experiments involving tensile tests at different strain rates (0.0003–1.0 s-1), stress triaxialities (0.33–0.95), temperatures (30–800 °C), and SHPB experiments (at 3000 and 8000 s-1). It explains the processes and step-by-step procedures for extracting the model parameters from the experimental results. A different approach is followed in arriving at fracture strain for extracting damage model parameters to suit fracture mechanic-based damage evolution available in the existing FEA codes. The constitutive and damage model parameters thus determined are validated through numerical simulations and comparison with three independent experiments viz. i) experiment of a plain tensile specimen, ii) tensile experiment of a notched specimen, and iii) hydrostatic burst experiment of a flat burst disc. The responses and failure patterns from numerical simulations agreed very well in all three experiments, thereby validating the determined model parameters. The determined model parameters can be utilised directly in the commercially available nonlinear explicit FEA codes. [ABSTRACT FROM AUTHOR]

Springback, buckling, and cracking are typical problems that take place during the stamping of titanium alloy sheets. Accuracy of material response characterization at moderate strain rates is an important factor for improving the adequacy of predictions of structures subjected to forming processes. In this paper, the deformation and fracture of alpha titanium alloys were studied using numerical simulations and the punch test at strain rates up to several hundred per second. Loading velocities from 0.5 to 10 m/s were realized during the spherical body penetration through a thin titanium plate. A viscoplastic constitutive model and damage model are used to describe the mechanical behavior of alpha titanium alloys at strain rates ranging from 10 to 103 s−1. Estimates of the residual stress of alpha titanium alloys are obtained using inverse simulation technique. It was found that amplitudes of residual stresses in CP-Ti after high speed punching are consistent with the increment of the yield stressas a result of strain hardening. Therefore, a comprehensive understanding of plastic deformation localization is essential for analyzing residual stresses in titanium alloys deformed at moderate strain rates. [ABSTRACT FROM AUTHOR]

The survivability of artillery projectile 155-mm Extended Range Full Bore Boat Tail (ERFB BT) inside gun barrel during gun launch mainly depends upon the mechanical properties of the shell body, boat tail and driving band materials. Any abrupt change in geometry of any one of these components can impair the structural integrity of the projectile, thereby resulting in malfunctioning of the projectile. Investigating the effect of abrupt change in geometry of the components is of much significance for assessing structural integrity. To investigate the effect of abrupt change in geometry of the components on structural failure, the notch tensile tests are performed to quantify the data on notch strength ratio (NSR), stress triaxiality and true fracture strain of the materials. To identify the mode of failure, the fractographic examination of the fracture surfaces is made. NSR is found more than unity; stress triaxiality determined by applying Bridgman's analysis reveals notch strengthening behavior of the materials. The fractographic examination shows that the shell body and boat tail materials fail in the combined ductile and brittle mode, whereas the driving band material fails by ductile mode. The outcome of the investigation confirms the load-carrying capacity and structural integrity of the projectile. [ABSTRACT FROM AUTHOR]

Accurately predicting the forming limit (FL) of sheet metals between equi-biaxial tension (EBT) and uniaxial tension (UT) is a research focus in sheet metal forming field. However, up to now, there is still a lack of an uncoupled ductile fracture criterion (DFC) which not only can predict the FL of sheet metals between EBT and UT accurately but also can be easily extended to other DFCs for bulk and sheet metals, preventing embedding only one uncoupled DFC into finite element analysis (FEA) software to satisfy the application requirements of fracture initiation prediction within different stress state ranges. The aim of this paper is to address the issue. The problems encountered in recently developed DFCs are firstly revealed and then a new uncoupled DFC is presented according to the analyses of void evolution of sheet metals. To fully understand the proposed DFC, parametric studies are conducted. In addition, the proposed DFC and four recently developed DFCs are employed to forecast the FL strains of three different sheet metals and the extensibility of the proposed DFC is studied. Research results show that the proposed DFC can not only forecast the FL of various sheet metals between EBT and UT reasonably but can also be easily extended to a unified uncoupled DFC for bulk and sheet metals, enabling the implantation of one DFC into FEA software to meet the application requirements within different stress state ranges. Moreover, the capability of the presented DFC to forecast FL in actual forming process is also verified. [ABSTRACT FROM AUTHOR]

Existing experimental data demonstrate a significant stress-state sensitivity of the properties for a wide class of solids, including metals, rocks, plastics, and other structural materials. Conventional parameters used to describe the material stress state are the stress triaxiality and the Lode angle. However, only dependence of the fracture criteria on the type of stress state is often considered. In the present paper, a version of constitutive relations is proposed which allow to describe the stress-state dependence of the material properties for the entire deformation process and thus to provide a more accurate approach to the estimation of the stress–strain state of solids. The proposed approach is exemplified with the solutions of various spherically symmetry problems for physically nonlinear solids. It can be noticed that the stress-state sensitivity taken into account may result in essential deviations of the solutions obtained from the predictions of the classical models. Although the constitutive relations are essentially nonlinear, in some particular cases, an analytic solution of the problem can be obtained. The approach discussed in this paper provides a relatively simple but realistic continuum model able to describe complicated deformation features of materials. [ABSTRACT FROM AUTHOR]

This paper investigates the failure strain as a dependence of the stress triaxiality and the Lode angle parameter for polyurethane rigid foams (PUR) of two densities (100 and 300 kg/m 3) . Tests were carried out in tension for various configurations, resulting in different states of stress triaxiality at various Lode angles in the critical areas. The failure strain was determined for each setup using finite element analysis, as the tests were replicated with numerical models. The displacement at failure recorded in the experiments was imposed for the models, determining the failure strain as a function of stress triaxiality and the Lode angle parameter. The results were validated through the analysis of the failure of sandwich structures with aluminium faces and PUR cores. [ABSTRACT FROM AUTHOR]

As a flexible sheet metal forming process, incremental sheet forming (ISF) has been extended to fabricate lightweight sheet metal components, and increasing the formability is one of the key topics. In the present work, a novel ISF process integrating an auxiliary sheet (ISF-AS) is proposed for the improvement in formability, and investigated by using commercially pure titanium (CP-Ti) as the target sheet (TS). The experimental results demonstrate that the fracture strain obtained by ISF-AS process is increased by 50.6% compared with conventional ISF (CISF), and the geometric accuracy by ISF-AS is less than that by CISF. To explore the deformation mechanism during ISF-AS process, an analytical model of stress triaxiality based on membrane analysis has been developed, which demonstrates that ISF-AS can further increase the hydrostatic compression stress and reduce the stress triaxiality of TS compared with CISF. The fracture morphologies indicate that the dimples by CISF and ISF-AS processes are both elongated along the circumferential direction, but there are more tiny dimples with uniform distribution on the fractured surface of ISF-AS. In addition, orange peels on the lower surface of the part can be obviously restricted by ISF-AS with the improved surface quality. [ABSTRACT FROM AUTHOR]

Tensile deformation behavior of the heat affected zone (HAZ) of Mod. 9Cr-1Mo weldment has been characterized. Different microstructural regions (coarse grain, fine grain and inter-critical) of the HAZ have been experimentally simulated using weld simulator. Flat tensile specimens, with desired microstructural region in the gage portion, were extracted from simulated bars prior and after post weld heat treatment (PWHT). The tensile tests have been carried out at ambient temperature. Parallelly, the local deformation characteristics of the HAZ have also been assessed using automated ball indentation tests to assess material specific parameters for constitutive model. Further, FEM analyses have been carried out to assess the effect of stress triaxiality on deformation behavior across the HAZ interfaces. The effect of triaxiality on the spread of plastic zone has been discussed. [ABSTRACT FROM AUTHOR]

Electromagnetic forming process could significantly increase the forming limit of aluminum alloy. However, high-speed fracture prediction of aluminum alloys is a major problem in the development of electromagnetic flanging process. In this study, notched specimen tensile tests with high-speed Digital Image Correlation system were conducted under the strain rate range from 0.001 to 100 s−1. A fracture model of AA5052 alloys which combined of an uncoupled fracture model, Gissmo damage evolution model and Johnson–Cook strain rate effect was established. Electromagnetic flanging experiments were conducted to verify the failure criteria effectiveness. Results showed that failure strain was significantly influenced by strain rate under various loading path. Compared with the experiments, the percentage error of established electromagnetic flanging process FEM model was less than 4%. The fracture model established could well predict notched specimen high-speed failure, and also accurately predict sheet failure model of electromagnetic flanging experiments and, thus, verified the effectiveness of the established dynamic failure criteria in electromagnetic flanging process. [ABSTRACT FROM AUTHOR]

Forged parts made of cold heading quality wire materials are used for automotive brake systems. In general, forged parts are limited in weight reduction due to strict configuration management, and thus cost reduction in the manufacturing process is a significant topic. In order to reduce the material cost, heat treatment-abbreviated material was applied and the formability of the processes was verified by stress triaxiality diagram. In this process, the limitations of the standard ductile fracture formula were verified. In addition, the causes of shape fixation and die life degradation were analyzed using numerical simulation. As a result, the process cost of EPB spindle parts has been minimized by redesigning the process, and changing the product shape and the die material. [ABSTRACT FROM AUTHOR]

A phenomenological ductile fracture model is proposed by a careful consideration of void nucleation, growth and coalescence during plastic deformation. Within the model framework, void nucleation is controlled by an equivalent plastic strain function. Void growth takes place through two ways, namely void dilation and void elongation, which are characterized by the normalized hydrostatic stress and normalized maximum shear stress, respectively. Void coalescence is characterized by the maximum shear stress. Aluminum alloy (AA) 6016-T6 sheets are selected to conduct ductile fracture (DF) experiments on specimens with different geometries, which can cover a wide range of stress states from simple shear to balanced biaxial tension. Subsequently, the new DF model is calibrated by using a robust hybrid numerical-experimental approach with a three-dimensional (3D) fracture surface constructed for AA 6016-T6. Ductile fracture data of other two aluminum alloys (AA 2024-T351 and AA 5083-O) are also used to evaluate DF model performance by establishing their 3D fracture surfaces. Finally, a cup drawing test is conducted and simulated as a case study showing how an applicable way of using the new model. Furthermore, the predictive accuracy of the proposed DF model for fracture initiation is compared with other three uncoupled models (modified Mohr–Coulomb criterion (MMC), Lou-Yoon-Huh model and Mu-Zang model) by ABAQUS/Explicit with a user subroutine (VUMAT), which shows a good performance of the proposed DF model. [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical investigations related to the block shear mechanism of double-lap welded connections. The experiment investigation includes 36 specimens composed of 3.0 mm and 6.0 mm thick mild carbon steel SS275 plates with varying block lengths and widths. It is found that the tension fracture in block shear of welded connection tends to be curved along the critical plane. The numerical results shows that the stress triaxiality effect in increasing the tensile stress over the critical tension plane, and thus the tension resistance component increases. This paper also examines the accuracy of various block shear strength equations given in the design codes as well as the literature. Topkaya's equation is found to be significantly more accurate than other block shear strength equations for the tested specimens. Nonetheless, it is recommended to use the reduced tensile coefficient to ensure both safe margin and the accuracy. [ABSTRACT FROM AUTHOR]

A double notched central hole, i.e., DNC specimen, which contains a center hole with a left side notch and a right side notch accompanying the slope α, is proposed to simultaneously achieve dual values of stress triaxiality and Lode parameter from one specimen in the present study. Analytical and numerical approaches are carried out under decent assumptions to characterize the plane strain behavior of DNC specimen along with the slope α. Quasi-static tensile tests with conventional specimens and DNC specimens revealed plastic strains at fracture for each specimen case in accordance with stress triaxiality and Lode parameter by digital image correlation. It is found that one DNC specimen successfully provides dual values of stress triaxiality and Lode parameter at the same time; therefore, it saves up to 50 % of experimental time and labor of conventional specimens. [ABSTRACT FROM AUTHOR]

Many metal materials possess the transition from strain localization to fracture, the so-called post-necking behavior, during large deformation under tensile load. It is crucial to understand and characterize the transition for the application of these materials. In this paper, the stress state dependence of the transition from strain localization to fracture of Ti–6.5Al–3.5Mo–1.5Zr–0.3Si alloy is characterized and analyzed by carrying out experiments and phase-field modeling. Firstly, tensile tests for smooth and notched round bars were conducted, in which the notched specimens have different notch radius. It was observed in the tests that the sharper the notch, the shorter the transition process, which can be explained as that high stress triaxiality would shorten the transition process. To further quantify the effects of stress triaxiality in the transition process, the phase-field fracture model involving the nucleation, growth and coalescence of micro-voids is developed to simulate and characterize the damage evolution observed in experiments. The simulations show that as the stress triaxiality increases, the material undergoes less plastic deformation, whether in the initiation of strain localization or the transition process. More interestingly, it is found that there exists a critical value of stress triaxiality, which can be considered the characteristic point of brittle-ductile transition. Above this point, the material has almost no plastic deformation before localization, and brittle fracture occurs directly. This work is meaningful for evaluating the safety of metal structures under complex loads. [ABSTRACT FROM AUTHOR]

The review paper covers an overview of the early and current research related to models for both solid and damage mechanics. It addresses the most well-known phenomenological metal plasticity and ductile fracture models in these fields for monotonic loading conditions. The paper commences with a comprehensive literature review outlining the history and current state of the art of the plasticity and ductile fracture models. Then, the paper explains the principal stresses, showing how they represent a metal yield surface. Because most yield functions involve the stress invariant, an extended explanation of stress invariants' space is extensively described. Moreover, a list of coupled and non-coupled plasticity models and ductile fracture criteria are thoroughly explained chronologically to show the emerging of stress triaxiality and Lode angle in models for solid and damage mechanics. The models presented in this paper assume the material's isotropy, homogeneity, and elastic-plastic behavior. Finally, two comparison tables demonstrating the most well-known phenomenal plasticity and fracture models for continuum mechanics are chronologically listed. [ABSTRACT FROM AUTHOR]

Aluminum alloy 6061-T6 (AA 6061-T6) extrusions have been widely applied in large-span reticulated shells. However, researches on behaviors of the aluminum alloy under large deformation and fracture by means of meso-mechanics are still insufficient. This paper focuses on the plastic and fracture behaviors of AA 6061-T6 extrusions over a wide range of stress states. Experiments on smooth and notched round bars, grooved plates and shear plates are conducted. It is observed that the yield stress decreases as the notch or groove radius decreases. The yield stress under plane strain or pure shear is lower than that under axisymmetric tension. In addition, true stress–true strain data obtained from tensile coupon tests overestimate the hardening behavior at large deformation. To fully describe these experimental observations, a new plastic model considering the pressure dependence, Lode angle effect, and hardening with post-necking correction is proposed. Regarding the ductile fracture, modified Mohr–Coulomb fracture model with damage-induced softening is adopted to predict crack initiation and propagation under different stress states. The material models of plasticity and fracture are numerically implemented into FE code ABAQUS/explicit by the material subroutine VUMAT. It is found that both the overall nominal stress–strain curves and fracture patterns for all specimens are well predicted by the material models. For practical engineering design, recommended reduced values of shear strength and high-triaxiality tensile strength of AA 6061-T6 extrusions are given. [ABSTRACT FROM AUTHOR]

The fracture failure of high-strength steel has an important relationship with the stress state. In order to predict the fracture failure of high-strength steel under different stress conditions, based on the void growth model (VGM), a fracture model which comprehensively considers the effect of stress triaxiality and the Lode parameter on fracture failure is proposed and is called LVGM. A batch of Chinese Q690D high strength steel round rods and plate shaped specimens reflecting different stress states were processed, and the monotonic tensile tests, the scanning electron microscopy tests and the finite element calculation were carried out to study the crack initiation of the specimens. The microscopic mechanism of the fracture damage of the specimens was analyzed. Based on the fracture test results of the specimens and the corresponding finite element analysis, the LVGM parameters of the Q690D high strength steel were calibrated. Finally, the LVGM was used to predict the crack initiation and fracture failure process of the specimens with initial gap. The prediction results are in good agreement with the experimental results, and the LVGM has better prediction accuracy than the VGM. [ABSTRACT FROM AUTHOR]

The ultra-low cycle fatigue (ULCF) fracture initiation caused by cyclic large plastic strain in structural steels is often the governing limit state in steel structures when subjected to strong earthquake actions. Based on the author's previous work, this paper presents the improved cyclic void growth model (CVGM) and degraded significant plastic strain (DSPS) model considering the dependence of cyclic damage degradation parameters on stress triaxiality. To this end, tests on circular notched specimens and coupon specimens made of Q345qC steel were conducted, and scanning electron microscopy studies were performed on fracture surfaces of specimens, analysis results of which show that the ULCF fracture of Q345qC steel exhibits the typical behaviour of "void nucleation, growth, and coalescence." The cyclic damage degradation parameters of CVGM and DSPS model were calibrated at different stress triaxialities based on experimental results of specimens and complementary finite element analysis, and empirical formulas were subsequently established between cyclic damage degradation parameters and stress triaxiality. Finally, detailed finite element analysis results demonstrate that the improved CVGM and DSPS model can predict ULCF fracture behaviour with higher accuracy in comparison with original models. [ABSTRACT FROM AUTHOR]

Various tensile strain capacity (TSC) prediction equations have recently been presented by many research organizations such as Pipeline Research Council International and ExxonMobil Corporation. The gas industry uses these equations to determine the allowable strain for the cracked pipe. However, these TSC prediction equations cannot be applied to pipes with other defects such as corrosion or mechanical damage. Corrosion defects are the most common type of defect in actual operating conditions, and thus, they are an essential element for evaluating pipe structural integrity as they are most frequently connected to accidents. Therefore, it is necessary to develop a TSC prediction equation for corroded pipes. In this paper, to propose a new TSC prediction equation for corroded pipes, we conducted parametric finite element (FE) analyses using fracture strain criteria. To determine the appropriate fracture strain criteria, we reviewed several methods to construct the fracture locus. Then, we conducted parametric FE analyses using this fracture locus by considering variables affecting structural integrity, such as corrosion depth, corrosion length, wrap angle, and pressure ratio. Lastly, we presented the TSC prediction equation using these analyses. [ABSTRACT FROM AUTHOR]

Ductile rupture of 13% Cr-4% Ni martensitic stainless steels was examined during tension testing in order to better understand the role of second phase particles in these materials. SEM fracture surface examinations revealed that micro-voids were initiated from inclusions, and these inclusions were characterized from metallographic polished sections. Effect of stress triaxiality on the growth and impingement of the micro-voids were examined using a modified model of Rice and Tracey. In the case of the cast and wrought versions, the true fracture strains predicted for the measured stress triaxiality values were in a good agreement with the measured ones. For the weld metals, only the contribution of the micro-void growth cannot explain the experimental results, and it shows that the matrix properties such as austenite content and hardness of martensite play a significant contribution. The magnitude of the final stress triaxiality ratio measured after rupture was also related to the inclusion characteristics. [ABSTRACT FROM AUTHOR]

Double-side multi-point incremental forming (DMISF) process combines local and progressive forming features with the advantages such as high forming precision, high production flexibility, and high fracture limit, so it is suitable to form complex aerospace parts and difficult-to-shape materials. High-strength aluminum alloy is widely used in aerospace fields, but its poor formability at room temperature limits its further development. Pulse current was introduced into DMISF process to improve the formability of high-strength aluminum alloy. So equipment for electrically assisted double-side multi-point incremental sheet forming (E-DMISF) process was set up. However, the E-DMISF process is a complicated electro-thermal-structure multi-field coupling process; the flow of the material in the forming process is very complicated. In this research, the hyperbolic truncated cone and hyperbolic truncated pyramid were chosen as study objects and the stress triaxiality was selected as the characteristic function of ductile fracture criterion. Based on all above, the fracture limit experiments and simulation in the E-DMISF process were performed and the fracture criterion was established correspondingly. The result indicates that the electric field could help enhance the fracture limit effectively. [ABSTRACT FROM AUTHOR]

The fracture of ductile materials such as Al6061-T6 usually starts from void nucleation. In this study, we investigated strengthening effect and stress triaxiality behavior in notched Al alloy specimens. Various specimens, one un-notched and two with different U-types of notch, one with large diameter (L-notched) and another with small diameter (S-notched), having the same width were selected. The distribution of strain in the full-field was examined using the digital image correlation (DIC) method. Under the tensile test, S-notched specimens showed a more pronounced strengthening effect than the L-notched specimens. The results of DIC confirmed that the notch tip of the S-notched specimen experienced high strain, while the L-notched specimen experienced high strain at the center. The maximum stress triaxiality moved rapidly from the notch tip to the center with the increase in notch radius over 10 mm. The results of the stress triaxiality analysis by finite element method were in good agreement with the above DIC measurement results and predicted the void generation and fracture sites in L-notched and S-notched specimens. [ABSTRACT FROM AUTHOR]

In this research, the ductile fracture of ultra-fine-grained copper was investigated. Ultra-fine-grained copper was produced using equal channel angular pressing process. During this process, the average grain size of the copper specimens decreases. Experiments have shown that stress state has significant effect on fracture behavior and should be included in the constitutive models. Therefore, the ductile failure was analyzed here by focusing on its relationship with the effect of hydrostatic pressure and Lode angle parameter. Tensile tests were performed on smooth and notched round bar specimens as well as doubly grooved samples. Moreover, the fracture surfaces were investigated by a scanning electron microscope. The experimental results reveal that the stress triaxiality and Lode angle parameter have a remarkable effect on the ductile fracture of the ECAPed specimens. However, the effect of stress triaxiality on ductility reduction is more significant than the effect of the Lode angle parameter. Also, the experimental results show the transition from the tensile ductile fracture to shear fracture in the ECAPed specimens. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

The increasing demand of energy prompts the petroleum industry exploitation activities to the Arctic region where the low temperature is a strong challenge, both for structural design and material selection. For structural materials exhibiting the Lüders plateau, it has been reported that lowering the temperature will increase the Lüders plateau length. In order to obtain a deep understanding of the Lüders plateau effect on ductile crack growth resistance, we performed numerical analyses with SENT specimens and the Gurson damage model. The Lüders plateau was simplified by keeping the flow stress constant and varying the plateau length. The results show that the existence of the Lüders plateau does not influence the initiation toughness, however, will alter the material’s fracture resistance significantly. It is found that the Lüders plateau effect is in general controlled by the stress triaxiality level in front of the crack tip. Both the strain hardening and the crack depth effects on resistance curves are alleviated due to the Lüders plateau. For materials with very small initial void volume fraction, the Lüders plateau effect is more pronounced. Since the Lüders plateau intensifies the crack driving force and may lower down crack resistance curve, special attention should be paid to the application of materials with the Lüders plateau in the Arctic. [ABSTRACT FROM AUTHOR]

Based on the critical voids expansion ratio criterion, the basic material mechanical parameters such as the strain hardening index n and the hardening coefficient K were introduced in it, and the critical voids expansion ratio criterion was modified. Firstly, the basic hydraulic bulging experiments for the AA6016-T4 sheet metal and AA6016-O sheet metal were performed. According to the comparisons of the experiment results and the simulation results of bulging height, the FEM (finite element model) and the parameters in the numerical simulation were verified accurate. Then, the material constants C1 and C2, which were in the modified criterion were confirmed based on the histories of stress and strain in the forming processes of the two materials, and the specific expression of the modified fracture criterion was obtained. Secondly, the experiments and the numerical simulations of three different hydroforming processes of the box part with a 6016-O aluminum alloy were carried out. By comparing the distribution tendencies of the wall thickness on the two different measurement paths, the numerical simulation results have a good agreement with the experiment results and the FEMs of the hydroforming of the box part were verified accurate. So, according to the numerical simulations, the stress and strain histories of all the nodes in the three different hydroforming processes were introduced into the modified ductile criterion. Then, the positions of the fracture points in the three different processes were predicted by the value of the A, which is the conversion form of the modified fracture criterion. Thirdly, the experiment results and the prediction results of the positions of the fracture points were compared, according to the error analysis between them, it is verified that the prediction of the forming limit of box parts with AA6016-O using the modified critical voids expansion ratio criterion is accurate. [ABSTRACT FROM AUTHOR]

Abstract Constitutive equations were calibrated to improve their application in assessing a stress field in front of a crack under the conditions of large strains and stress triaxiality. The Bai–Wierzbicki method was adopted, and certain changes and new terms were introduced to incorporate material softening. Five shapes of specimens were tested to cover a wide range of stress triaxiality conditions and Lode factors. Tests were performed at three different temperatures, namely, +20 °C, –20 °C, and –50 °C, and on three different materials obtained by three different heat treatments of S355JR steel. [ABSTRACT FROM AUTHOR]

In this work, strain based fracture forming limit curve (FFLC) of advanced high strength (AHS) steel grade 980 was determined by means of experimental Nakajima stretch-forming test and tensile tests of samples under shear deformation. During the tests, a digital image correlation (DIC) technique was applied to capture the developed strain histories of deformed samples up to failure. The gathered fracture strains from different stress states were used to construct the FFLC. Subsequently, the FFLC in the strain space was transformed to a principal stress space by using plasticity theories. As a result, the fracture forming limit stress curve (FFLSC) of examined steel was obtained. Furthermore, fracture locus (FL) as a relationship between stress triaxialities and critical plastic strains was determined. Hereby, two anisotropic yield functions, namely, the Hill’48 and Yld89 model were taken into account and their effects on the calculated curves were investigated. To verify the applicability of the obtained limit curves, rectangular cup drawing test and forming tests of so-called Diabolo and mini-tunnel samples were performed. Obviously, the FFLSCs and FLs more accurately described the failure occurrences of 980 steel sheets than the FFLCs. In addition, it was found that the drawing depths predicted by the FLs and the Yld89 yield criterion slightly better agreed with the experimental results than those from the FFLSCs and the Hill’48 model, respectively. [ABSTRACT FROM AUTHOR]

Due to its attractive mechanical properties, aluminum 2024 is widely used in aircraft manufacturing industries, especially as fiber metal laminates, such as GLARE. In the present work, a series of experiments for different stress triaxialities are used to study the ductile damage of Al 2024 considering continuum damage mechanics (CDM). Stress triaxiality is produced using notched specimens. The main objective of the present study is to predict the local equivalent plastic strain to fracture and introducing a relation which describes the effect of stress triaxiality factor (TF) on it in the medium range of stress triaxiality. Hence, a nonlinear damage model is utilized for Al 2024 and its parameters are determined by an experimental/numerical/optimization procedure using tensile test on plain specimens. The experiments showed that for large notch specimens (Al-NL) and medium notch samples (Al-NM) fracture started from the center of the notch root of the specimens, whereas for small notched specimens (Al-NS) the failure initiated from the notch root surface. Finite element simulations are performed using the presented nonlinear damage model and are compared with the experimental data. Results show that the proposed damage model can predict the damage evolution for different stress triaxialities. [ABSTRACT FROM AUTHOR]

Monotonic deformation behavior of ferrite-martensite dual phase steels with martensite volume of 13-43% have been analyzed in the current investigation using micromechanics based finite element simulation on representative volume elements. The effects of martensite volume fraction on the strain partitioning behavior between soft ferrite matrix and hard martensite islands in dual phase steels during tensile deformation have been investigated. As a consequence of strain incompatibility between hard martensite and soft ferrite phases, inhomogeneous deformation and finally deformation localization occur during tensile deformation. Restricted local deformation in ferrite phase caused by the adjacent martensite islands triggers the local stress triaxiality development. As the martensite volume fraction increases, the local deformation restrictions in ferrite phase also increases and which results in higher stress triaxiality development. Similarly the strain partitioning behavior between ferrite matrix and martensite island is also influenced by the volume fraction of martensite. The strain partitioning coefficient increases with increasing martensite volume fraction. [ABSTRACT FROM AUTHOR]

Gurson-type models have been widely used to predict failure during sheet metal forming process. However, a significant limitation of the original GTN model is that it is unable to capture fracture under relatively low stress triaxiality. This paper focused on the fracture prediction under this circumstance, which means shear-dominated stress state. Recently, a phenomenological modification to the Gurson model that incorporates damage accumulation under shearing has been proposed by Nahshon and Hutchinson. We further calibrated new parameters based on this model in 22MnB5 tensile process and developed the corresponding numerical implementation method. Lower stress triaxiality were realized by new-designed specimens. Subsequently, the related shear parameters were calibrated by means of reverse finite element method and the influences of new introduced parameters were also discussed. Finally, this shear modified model was utilized to model the small punch test (SPT) on 22MnB5 high strength steel. It is shown that the shear modification of GTN model is able to predict failure of sheet metal forming under wide range of stress state. [ABSTRACT FROM AUTHOR]

A forming limit diagram (FLD) is commonly used as a useful means for characterising the formability of sheet metal forming processes. In this study, the Nakajima test was used to construct the forming limit curve at necking (FLCN) and fracture (FLCF). The results of the FLCF are compared with incremental sheet forming (ISF) to evaluate the ability of the Nakajima test to describe the fracture in ISF. Tests were carried out to construct the forming limit diagram at necking and fracture to cover the strain states from uniaxial tension to equi-biaxial tension with different stress triaxialities--from 0.33 for uniaxial tension to 0.67 for equi-biaxial tension. Due to the fact that the Gurson-Tvergaard-Needleman (GTN) model can be used to capture fracture occurrence at high stress triaxiality, and the shear modified GTN model (Nahshon-Hutchinson's shear mechanism) was developed to predict the fracture at zero stress or even negative stress triaxiality, the original GTN model and shear modified GTNmodel may be not suitable to predict the fracture in all samples of the Nakajima test as some samples are deformed under moderate stress triaxiality. In this study, the fractures are compared using the original GTN model, shear modified GTN model and the Nielsen-Tvergaard model with regard to stress triaxiality. To validate the ability of these models, and to assess which model is more accurate in predicting the fracture with different stress triaxialities, finite element (FE) simulations of the Nakajima test were compared with an experimental results to evaluate the applicability of the Nakajima test to characterise the fracture from ISF. The experimental and FE results showed that the shear modified GTN model could predict the fracture accurately with samples under uniaxial tension condition due to low stress triaxiality and that the original GTN model is suitable for an equi-biaxial strain state (high stress triaxiality), whereas the stress triaxiality modified GTN model should be considered for samples which have moderate stress triaxiality (from plain strain to biaxial strain). The numerical and experimental FLCF of pure titanium from the Nakajima test showed a good agreement between the experimental and numerical results of ISF. [ABSTRACT FROM AUTHOR]

Local mechanical properties in aluminum cast components are inhomogeneous as a consequence of spatial distribution of microstructure, e.g., porosity, inclusions, grain size and arm spacing of secondary dendrites. In this work, the effect of porosity is investigated. Cast components contain voids with different sizes, forms, orientations and distributions. This is approximated by a porosity distribution in the following. The aim of this paper is to investigate the influence of initial porosity, stress triaxiality and Lode parameter on plastic deformation and ductile fracture. A micromechanical model with a spherical void located at the center of the matrix material, called the representative volume element (RVE), is developed. Fully periodic boundary conditions are applied to the RVE and the values of stress triaxiality and Lode parameter are kept constant during the entire course of loading. For this purpose, a multi-point constraint (MPC) user subroutine is developed to prescribe the loading. The results of the RVE model are used to establish the constitutive equations and to further investigate the influences of initial porosity, stress triaxiality and Lode parameter on elastic constant, plastic deformation and ductile fracture of an aluminum die casting alloy. [ABSTRACT FROM AUTHOR]

The effect of the stress state on the fracture locus function of the 50 vol.% Al/SiC metal matrix composite at high temperature is studied. The value of fracture locus function is quantitatively characterized by the amount of shear strain accumulated prior to the moment of failure. Nondimensional invariant parameters are used as characteristics of the stress state, namely, the stress triaxiality k and the Lode-Nadai coefficient μ showing the form of the stress state. Besides conventional testing for tension, compression and torsion of smooth cylindrical specimens, the complex of mechanical tests includes a new type of testing, namely, that for bell-shaped specimens. These kinds of testing enable one to study fracture strain under monotonic deformation in the ranges μ = 0 ... + 1 and k = − 1.08...0 without using high-pressure technologies. The stress-strain state during specimen testing is here evaluated from the finite element simulation of testing in ANSYS. The tests were performed at a temperature of 300 °C and shear strain rate intensity Η = 0.1; 0.3; 0.5 1/s. The test results have offered a fracture locus, which can be used in models of damage mechanics to predict fracture of the material in die forging processes. [ABSTRACT FROM AUTHOR]

In the present study, the effects of pipe geometries, material properties and loading conditions on crack-tip constraints of pipes with circumferential Through-wall crack (TWC) were investigated via systematic 3-dimensional (3-D) Finite element (FE) analyses. The crack-tip constraints were quantified by Q-stress, and to characterize the elastic-plastic strain hardening material behavior, Ramberg-Osgood (R-O) material was employed. Based on the FE results, it was observed that crack-tip constraints of pipes with TWC were dependent on crack length and thickness of pipe, however, the effects of each variables decreased as either thickness of pipe becomes thinner or crack length becomes longer. Moreover, the effects loading modes on Q-stresses for thin-walled pipes with TWC are negligible. Finally, the present Q-stresses of pipes were compared with those of Curved wide plate (CWP) in tension to address the similarity of crack-tip constraints between pipe and CWP, which could be used to produce the CWP to measure the fracture toughness of pipes accurately. [ABSTRACT FROM AUTHOR]

The finite element method based on GTN ductile damage mechanics model has been used to investigate the interaction effects of geometry and material constraints on fracture resistance behavior of bi-material interfaces. The geometry constraint is changed by changing the specimen width W, and the material constraint is changed by changing the work hardening mismatch. The main findings of this work are that the material constraint effect on fracture resistance of bi-material interfaces is related to geometry constraint, and there exists interaction between them. For lower geometry constraint, the material constraint effect on fracture resistance is insignificant. Under the condition of middle geometry constraint, the material constraint effect on fracture resistance is the most significant. With further increasing geometry constraint, the fracture resistance behavior of the interfaces is gradually dominated by the higher geometry constraint, and the material constraint effect becomes weaken. These results are analyzed by the stress triaxiality levels ahead of crack tips and crack path deviation. [ABSTRACT FROM AUTHOR]

The maximum principal stress, von Mises equivalent stress, equivalent creep strain, stress triaxiality in dissimilar metal welded joints between austenitic (HR3C) and martensitic heat-resistant steel (T91) are simulated by FEM at 873 K and under inner pressure of 42.26 MPa. The results show that the maximum principal stress and von Mises equivalent stress are quite high in the vicinity of weld/T91 interface, creep cavities are easy to form and expand in the weld/T91 interface. There are two peaks of equivalent creep strains in welded joint, and the maximum equivalent creep strain is in the place 27-32 mm away from the weld/T91 interface, and there exists creep constrain region in the vicinity of weld/T91 interface. The high stress triaxiality peak is located exactly at the weld/T91 interface. Accordingly, the weld/T91 interface is the weakest site of welded joint. Therefore, using stress triaxiality to describe creep cavity nucleation and expansion and crack development is reasonable for the dissimilar metal welded joint between austenitic and martensitic steel. [ABSTRACT FROM AUTHOR]

Stress state is a main parameter within fracture mechanics. It has a major influence on different phenomena, namely those involving diffusion, plastic deformation, and brittle fracture. As is well-known, in the near-surface regions of a crack front, the plane stress state dominates, while at interior positions the plane strain state prevails. The main objective here is to examine the extent of surface regions in through-cracked planar geometries subjected to cyclic loading. Two constitutive material models were developed to characterise the stress state along the crack front. A new criterion based on the h stress triaxiality parameter was proposed to define the transition between surface and near-surface regions. Finally, a linear relation between the stable value of the extent of surface region and the maximum stress intensity factor was established. [ABSTRACT FROM AUTHOR]

In this study, creep experiments on smooth and circumferential V-type notched round bars were conducted in GH3536 Ni-based superalloy at 750 °C to identify notch strengthening effect in notched specimens. FE analysis was carried out, coupled with continuum damage mechanics (CDM), to analyze stress distribution and damage evolution under multiaxial stress state. The creep deformation of smooth specimens and the rupture life of both smooth and notched specimens showed good agreement between experimental results and FE analysis predictions; the creep rupture life for the notched specimen was successfully predicted via the 'skeletal point' concept. Both creep damage analysis and the observed fracture morphology suggest that creep rupture started first at the root in the V-type notched specimens, and shifted to the region close to the notch root when the notch was relatively shallow compared to U-type notched specimens. [ABSTRACT FROM AUTHOR]

In this work, to study the effects of stress triaxiality, temperature, and strain rate on the fracture behaviors of a single-crystal Nickel-base superalloy, a series of experiments over a temperature range of 293 to 1373 K, strain rate range of 0.001 to 4000/s, and stress triaxiality range of −0.6 to 1.1 are conducted. Anomalous peak of stress is noticed in the yield stress versus temperature curves, and strain rate effect on the anomalous peak of yield stress is analyzed. The anomalous peak shifts to higher temperature as the strain rate increases. Then the effects of stress triaxiality, temperature, and strain rate on its fracture behaviors, including strain to fracture, path of crack propagation, and fracture surface, are observed and analyzed. A valley of the fracture strain is formed in the fracture strain versus temperature curve over the selected temperature range. The micrograph of fracture surface is largely dependent on the temperature, stress triaxiality, and strain rate. Finally, the original Johnson-Cook (J-C) fracture criterion cannot describe the effect of stress triaxiality and temperature on the fracture behaviors of single-crystal Nickel-base superalloy. A modified J-C fracture criterion is developed, which takes the anomalous stress triaxiality and temperature effects on the fracture behaviors of single-crystal Nickel-base superalloy into account. [ABSTRACT FROM AUTHOR]

Experimental and numerical investigations of the failure strain of aeronautical 2024-T3 aluminum were conducted. Experiments on the Double notched tube (DNT) specimen loaded in combined tension and torsion were applied to an aluminum alloy for the first time. Numerical analysis showed that the specimen exhibited uniformity in stress-strain as plastic strain developed. Low triaxiality values and a wide range of Lode parameter values were obtained at failure conditions. The failure strain of 2024-T3 aluminum showed strong dependence on the Lode parameter in agreement with the observations reported by other authors. The use of the DNT specimen was proven to be efficient in calibrating the ductile failure model of aluminum alloys. [ABSTRACT FROM AUTHOR]

To better understand the fracture behavior of TA15 titanium alloy during hot forming, three groups of experiments were conducted to investigate the influence of deformation temperature, strain rate, initial microstructure, and stress triaxiality on the fracture behavior of TA15 titanium alloy. The microstructure and fracture surface of the alloy were observed by scanning electronic microscopy to analyze the potential fracture mechanisms under the experimental deformation conditions. The experimental results indicate that the fracture strain increases with increasing deformation temperature, decreasing strain rate, and decreasing stress triaxiality. Fracture is mainly caused by the nucleation, growth, and coalescence of microvoids because of the breakdown of compatibility requirements at the α/β interface. In the equiaxed microstructure, the fracture strain decreases with decreasing volume fraction of the primary α-phase (α) and increasing α/β-interface length. In the bimodal microstructure, the fracture strain is mainly affected by α-lamella width. [ABSTRACT FROM AUTHOR]

The purpose of this study is to propose a method to correlate micro-structural characteristics of two-phase steel with structural performance in terms of ductile crack growth resistance (R-curve). For this purpose, a meso-scopic simulation method is proposed to predict two types of ductile properties of two-phase steel that control the R-curve from micro-structural characteristics. The R-curve of three-point bend specimen with fatigue pre-crack predicted by a macro-scopic simulation method that we have proposed, in which these two types of ductile properties obtained by the proposed meso-scopic methods are implemented, is in good agreement with experimental result. [ABSTRACT FROM AUTHOR]

A physics-based, uncoupled damage model is calibrated using cylindrical notched round tensile specimens made of Ti5553 and Ti-6Al-4V alloys. The fracture strain of Ti5553 is lower than for Ti-6Al-4V in the full range of stress triaxiality. This lower ductility originates from a higher volume fraction of damage sites. By proper heat treatment, the fracture strain of Ti5553 increases by almost a factor of two, as a result of a larger damage nucleation stress. This result proves the potential for further optimization of the damage resistance of the Ti5553 alloy. The damage model is combined with an elastoviscoplastic law in order to predict failure in a wide range of loading conditions. In particular, a specific application involving bolted sectors is addressed in order to determine the potential of replacing the Ti-6Al-4V by the Ti5553 alloy. [ABSTRACT FROM AUTHOR]

A tubular tension-torsion specimen is proposed to characterize the onset of ductile fracture in bulk materials at low stress triaxialities. The specimen features a stocky gage section of reduced thickness. The specimen geometry is optimized such that the stress and strain fields within the gage section are approximately uniform prior to necking. The stress state is plane stress while the circumferential strain is approximately zero. By applying different combinations of tension and torsion, the material response can be determined for stress triaxialities ranging from zero (pure shear) to about 0.58 (transverse plane strain tension), and Lode angle parameters ranging from 0 to 1. The relative displacement and rotation of the specimen shoulders as well as the surface strain fields within the gage section are determined through stereo digital image correlation. Multi-axial fracture experiments are performed on a 36NiCrMo16 high strength steel. A finite element model is built to determine the evolution of the local stress and strain fields all the way to fracture. Furthermore, the newly-proposed Hosford-Coulomb fracture initiation model is used to describe the effect of stress state on the onset of fracture. [ABSTRACT FROM AUTHOR]

In this contribution, the effect associated with stress triaxiality on ductile damage evolution in high purity nickel has been investigated from both experimental and theoretical points of view. Tensile tests on smooth and notched round bar specimens were performed to calibrate the fracture strain in a wide range of stress triaxiality. The capability of the Gurson model to reproduce and predict physical failure behaviour was examined. It was shown that stress triaxiality played a major role on damage evolution as demonstrated by the progressive reduction of material ductility under increasing triaxial states of stress. [ABSTRACT FROM AUTHOR]

This paper analyzes the role of microstructural anisotropy generated by cold drawing in the hydrogen-assisted fracture of progressively drawn pearlitic steel notched bars. Very different notched geometries were used to generate quite distinct stress triaxiality distributions (and thus very different constraint levels) in the vicinity of the notch tip, and fracture surfaces were classified in accordance with three micromechanical models of hydrogen-assisted micro-damage on the basis of the micro-fracture maps assembled by scanning electron microscopy over the fractured area of the notched specimens. [ABSTRACT FROM AUTHOR]