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The current paper discusses concepts for implementing distinct edge dislocations into continua. Such dislocation models are successful, if they correctly predict both the stress- and displacement field around the dislocation line and the driving force on the dislocation in the presence of an external stress state. In addition, it is desired to realize the dislocation model by finite element programs. It is shown that the dislocation models available in literature do not fulfill these conditions, since they do not yield the correct driving force terms. Additional defect structures are investigated in order to work out a more successful dislocation model. Several methods are applied to derive the driving force on the dislocation for each model, (i) the configurational force concept, (ii) a thermodynamic concept based on the interaction energy, (iii) a relationship based on conservation integrals and the dislocation density. The results are compared to the classical Peach-Koehler solution. Two different procedures are worked out to correctly model a single edge dislocation, a numerically very simple method in form of two strips with prescribed eigenstrain components, which are considered consecutively, and a numerically more sophisticated concept, denominated as “cut-displace-glue” procedure.

Talcum reinforced polypropylene was enhanced with a soft type of polypropylene in order to increase the impact strength and damage tolerance of the material. The soft phase was incorporated in the form of continuous interlayers, where the numbers of layers ranged from 64 to 2048. A blend with the same material composition (based on wt% of the used materials) and the pure matrix material were investigated for comparison. A plateau in impact strength was reached by layered architectures, where the matrix layer thickness was as small or smaller than the largest talcum particles. The most promising layered architecture, namely, 512 layers, was subsequently investigated more thoroughly using instrumented Charpy experiments and tensile testing. In these tests, normalised parameters for stiffness and strength were obtained in addition to the impact strength. The multilayered material showed remarkable impact strength, fracture energy and damage tolerance. However, stiffness and strength were reduced due to the addition of the soft phase. It could be shown that specimens under bending loads are very compliant due to a stress-decoupling effect between layers that specifically reduces bending stiffness. This drawback could be avoided under tensile loading, while the increase in toughness remained high.

Twisted plywood architectures can be observed in many biological materials with high fracture toughness, such as in arthropod cuticles or in lamellar bone. Main purpose of this paper is to analyze the influence of the progressive rotation of the fiber direction on the spatial variation of the crack driving force and, thus, on the fracture toughness of plywood-like structures. The theory of fiber composites is used to describe the stiffness matrix of a twisted plywood structure in a specimen-fixed coordinate system. The driving force acting on a crack propagating orthogonally to the fiber-rotation plane is studied by methods of computational mechanics, coupled with the concept of configurational forces. The analysis unfolds a spatial variation of the crack driving force with minima that are beneficial for the fracture toughness of the material. It is shown that the estimation of the crack driving force can be simplified by replacing the complicated anisotropic twisted plywood structure by an isotropic material with appropriate periodic variations of Young’s modulus, which can be constructed based either on the local stiffness or local strain energy density variations. As practical example, the concepts are discussed for a specimen with a stiffness anisotropy similar to lamellar bone. Statement of Significance Twisted plywood-like structures exist in many natural fiber composites, such as bone or insect carapaces, and are known to be very fracture resistant. The crack driving force in such materials is analyzed quantitatively for the first time, using the concept of configurational forces. This tool, well established in the mechanics of materials, is introduced to the modeling of biological material systems with inhomogeneous and anisotropic material behavior. Based on this analysis, it is shown that the system can be approximated by an appropriately chosen inhomogeneous but isotropic material for the calculation of the crack driving force. The spatial variation of the crack driving force and, especially, its local minima are essential to describe the fracture properties of twisted plywood structures.

Lamellar bone is known to be the most typical structure of cortical bone in large mammals including humans. This type of tissue provides a good combination of strength and fracture toughness. As has been shown by John D Currey and other researchers, large deformations are associated with the appearance of microdamage that optically whitens the tissue, a process that has been identified as a contribution to bone toughness. Using finite-element modelling, we study crack propagation in a material with periodic variation of mechanical parameters, such as elastic modulus and strength, chosen to represent lamellar bone. We show that a multitude of microcracks appears in the region ahead of the initial crack tip, thus dissipating energy even without a progression of the initial crack tip. Strength and toughness are shown to be both larger for the (notched) lamellar material than for a homogeneous material with the same average properties and the same initial notch. The length of the microcracks typically corresponds to the width of a lamella, that is, to several microns. This simultaneous improvement of strength and toughness may explain the ubiquity of lamellar plywood structures not just in bone but also in plants and in chitin-based cuticles of insects and arthropods.

The introduction of thin interlayers with low yield stress can greatly improve the strength and the fracture toughness of inherently brittle materials. The reason is that the spatial yield stress variation affects the crack driving force, which strongly decreases when the crack tip is located in the interlayer region, near the boundary to the hard matrix material. This can lead to crack arrest. The material inhomogeneity effect appears without previous delamination of the interlayer. The decisive parameters influencing the effect are the interlayer spacing (the wavelength of the yield stress variation), the interlayer thickness and the yield stress ratio between interlayer and matrix. Based on numerical simulations with the configurational forces concept, it is demonstrated how the architectural parameters of the multilayer must be chosen in order to enhance the fracture stress and the fracture toughness of the material. An iterative procedure is proposed to find the optimum configuration. It is found that the optimum wavelength is inversely proportional to the square of the applied stress. A similar relation is given for composites with spatial variations in Young's modulus.

The evolution of the irradiation embrittlement of nuclear pressure vessel steels is determined experimentally using special specimen geometries. Such sub-sized w-shape eccentrically-loaded single edge cracked tension specimens are employed due to mounting and handling requirements. Stress intensity factor solutions are available in the literature for this geometry; however, they are inaccurate for smaller crack lengths. Therefore, new approximate solutions are presented in this work to determine the stress intensity factor for such a w-shape tension specimen for a wide range of crack lengths (0.05

The effect of local deformation on the fracture behaviour of TiAl alloys was investigated. Roller indentations impressed parallel to the crack plane significantly improve the fracture toughness. The residual strains present in the indentation zone were characterized by X-ray diffraction and modelled using finite element (FE) calculations. The experimentally observed macrostrains exhibit remarkable crystallographic anisotropies and are unequally shared between the major alloy constituents. The mechanisms behind the observed toughening have been discussed in terms of the residual strains and factors improving the crack tip plasticity. With regard to intended high-temperature applications, the temperature retention of the toughening effect was studied.

In a multilayered structure with a crack, a spatial change in the mechanical properties of the material strongly influences the crack driving force. This material inhomogeneity effect can be utilized to improve the fracture toughness of a given structure by inserting thin, soft interlayers into the material. The effectiveness of this procedure has been demonstrated on high-strength materials, such as metallic alloys and ceramics. It is shown in this article that the material inhomogeneity effect can be also successfully applied to polymers and that it is possible to predict the improvement in fracture toughness by a numerical analysis. First, a numerical case study based on the configurational force concept is performed on a brittle polymer matrix with interlayers made of materials with different strength and Young’s modulus. After selecting the most appropriate interlayer material, a composite is fabricated, which contains a single interlayer. Fracture toughness experiments show approximately 7 times higher fracture toughness for the composite in comparison to the homogeneous matrix material. Numerical fracture mechanics tests are performed on homogeneous and composite material using the cohesive zone model for crack growth simulation. A procedure to calibrate the cohesive zone parameters is worked out, which is relatively easy for the homogeneous material, but more sophisticated for the composite material. The numerical analysis provides a tool for predicting the fracture toughness of multilayered polymer composites.

A material with spatial variation in the elastic modulus E can have a much higher apparent fracture resistance and fracture stress than a comparable homogeneous material. The effect occurs due to the strong decrease of the crack driving force, which leads to crack arrest when the crack tip is located in the region with low elastic modulus. From the results of exemplary numerical studies and simple fracture mechanical considerations, models are derived in order to predict the fracture stress and fracture toughness of the inhomogeneous materials. It is shown that high values of fracture stress and fracture toughness can be reached if the amplitude of the E variation is high enough to provide crack arrest and the wavelength of the E variation is small. The beneficial effect of material property variations also occurs if the width of the compliant region is very thin and the loss in stiffness of the structure is almost negligible. The concept is applicable for various types of composite materials; examples are presented.

The so-called material inhomogeneity effect, which influences the crack driving force in inhomogeneous materials, has recently been found to contribute to the excellent behavior of some fracture resistant biomaterials. The current study aims to transfer these findings to engineering materials, by experimentally investigating the fracture behavior of multilayers consisting of a high-strength aluminum alloy and thin, soft polymer interlayers. Structures in crack divider and crack arrester (CA) configuration are tested. The results show that the structures in CA configuration exhibit a tremendously improved fracture resistance compared to the homogeneous bulk material. The reason is that cracks are completely arrested in the soft interlayers. This effect appears without delamination, i.e. it is basically different from the well-known delamination effect on weak interlayers.

We demonstrate in this paper that commercially available printing paper can reach very high fracture toughness, comparable to that of steel, simply due to a special arrangement of the paper sheets with respect to the crack. Fracture mechanics experiments are conducted on single sheets of paper as well as on multilayer specimens in crack divider and crack arrester configuration. It is demonstrated that an arrangement in crack arrester configuration leads to an increase of the fracture toughness by a factor ten. An explanation of the effect is given and the transferability to other materials is discussed.

The concept of configurational forces is applied to demonstrate the application of the concept of configurational forces in the numerical simulation of crack growth and fracture processes. It is shown, how material property variations at an interface affect the crack driving force and how the criterion of maximum dissipation is used to evaluate the direction of crack propagation. Fatigue crack growth experiments were conducted on diffusion welded bimaterial specimens consisting of a high-strength steel and soft ARMCO iron. Two cases are considered: (1) specimens with an interface perpendicular to the initial crack orientation, and (2) specimens with an inclined interface. The numerical simulation with the concept of configurational forces show that not only variations of the elastic modulus and/or the yield stress have a tremendous influence on the crack driving force, the crack growth rate, and the curvature of the crack path, but also the thermal residual stresses that resulted from a rather small difference of the coefficient of thermal expansion.

Finite element computations are performed to analyze the phenomena of edge cracking and crack bifurcation in two ceramic laminates composed by tensile thick layers and compressive thin layers. The difference between these two laminates is the thickness of the compressive thin layers. Experimental results performed by one of the authors in previous works show that edge cracks exist in only one laminate, while crack bifurcation occurs in both laminates under bending. To understand the cracking phenomena observed in experiments, the energy release rates are calculated. Numerical results show that the initiation of crack bifurcation can be explained by the near-tip J-integral, provided that micro-cracks exist near the crack tip.

The effect of thermal residual stresses in bimaterial structure with initial crack located near a sharp interface is discussed in this paper. Bimaterial compact tension (CT) specimen is used in the analysis, and the residual stresses are introduced by cooling of the specimen. The residual stresses affect the stress and strain fields near the crack tip, and the crack-driving force is different compared with that in the homogeneous material without residual stresses. This difference can be quantitatively expressed through an additional crack-driving force term—the material inhomogeneity term, Cinh. In this paper, it is evaluated using the post-processing procedure based on the concept of configurational forces, following a finite-element analysis. The results indicate that accurate numerical analysis of pre-cracked bimaterials should include the effect of thermally induced residual stresses. This effect cannot be neglected, even for bimaterials with homogeneous mechanical properties and inhomogeneity in thermal properties only (e.g. welded joints of ferritic and austenitic steel). Based on the obtained results, data from this study can be used in engineering practice to improve integrity and work safety of various inhomogeneous structures.

Powder-metallurgy metal matrix composites (MMCs) with Al-6061 matrix and SiC-particles are analyzed by means of in situ tensile tests in the scanning electron microscope and automatic local deformation analyses. The particle size (10 and 100 μm) and the particle volume fraction (10% and 20%) are varied. For comparison the pure matrix material is also tested. The formation of the shear bands with increasing load is studied, and the differences in the shear band evolution in the different materials are worked out. Cracks are initiated by particle fracture and by matrix/particle decohesion. The crack tip opening displacements (COD) at the particle failure sites are determined, as well as the critical COD-values for particle cracks propagating into the matrix material. Qualitative relations between the global ductility of the MMCs and the deformation and damage behavior, both observed at the micro-scale, are worked out.

A material inhomogeneity in the direction of crack extension causes a difference between the near-tip crack driving force, Jtip, and the nominally applied far-field crack driving force, Jfar. This difference can be quantified by a material inhomogeneity term, Cinh, which is evaluated by a post-processing procedure to a conventional finite element stress analysis. The magnitude of the material inhomogeneity term is evaluated for cracks in an inhomogeneous welded joint made of a high-strength low-alloy steel. Both a crack proceeding from the under-matched (UM) to the over-matched (OM) and from the OM to the UM weld metal are treated. The effects of the inhomogeneity of the different material parameters (modulus of elasticity, yield strength, and strain hardening exponent) on Cinh and Jtip are systematically studied. The results demonstrate that the material inhomogeneity term is primarily influenced by the inhomogeneity of the yield strength. A crack growing towards an OM/UM interface experiences an accelerated crack growth rate or a pop-in, an UM/OM interface leads to a reduced crack growth rate or a crack arrest. The application of global assessment methods of the mismatch effect which are included in the Engineering Treatment Model (ETM) or in the Structural Integrity Assessment Procedures for European Industry (SINTAP) is discussed.

A new model for the estimation of the micro-toughness in ductile fracture is presented. Micro-toughness is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. Stereophotogrammetric measurements of the height and width of dimples on ductile fracture surfaces are used in conjunction with the model to determine the micro-toughness. A finite element model is used to validate the analytical model. With the new model the ratio between the micro-toughness as related to the fracture surface topology and the global fracture toughness (J-integral) values become physically reasonable. The model is applied to structural steels and a metal matrix composite. Implications to computational fracture mechanics models are discussed.

A procedure to predict the fracture toughness of a ceramic multilayer composite made of different phases is presented. The procedure requires experiments to measure the intrinsic fracture toughness of the phases and to determine the required material data. The numerical modeling includes a conventional finite element stress analysis and the calculation of the crack driving force based on the concept of configurational (material) forces. The procedure yields the fracture toughness of the composite as a function of the crack length. A bending bar consisting of layers made of alumina and an alumina–zirconia composite is investigated. The bar has a crack perpendicular to the interfaces. The spatial variations of both the thermal residual stresses and the elastic modulus induce shielding and anti-shielding effects on the crack, which are quantified. The numerically predicted fracture toughness is compared with the experimental values.

An Al6061-20%Al 2 O 3 powder metallurgy (PM) metal matrix composite (MMC) with a strongly clustered particle distribution is subjected to equal channel angular pressing (ECAP) at a temperature of 370 °C. The evolution of the homogeneity of the particle distribution in the material during ECAP is investigated by the quadrat method. The model proposed by Tan and Zhang [Mater Sci Eng 1998;244:80] for estimating the critical particle size which is required for a homogeneous particle distribution in PM MMCs is extended to the case of a combination of extrusion and ECAP. The applicability of the model to predict a homogeneity of the particle distribution after extrusion and ECAP is discussed. It is shown that ECAP leads to an increase of the uniformity of the particle distribution and the fracture toughness.

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T-max and the separation energy, Gamma) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality. (c) 2005 Elsevier Ltd. All rights reserved.

— A new tool is presented to investigate cleavage fracture surfaces. It is based on the combined techniques of crystal orientation measurements using the Electron Back-Scatter Diffraction (EBSD)-technique and 3-dimensional surfaces reconstruction by an Automatic Surface Reconstruction System (ASRS). With this tool we can perform crystallographic fractometry of cleavage fracture facets of polycrystals within the limits of the resolution of a Scanning Electron Microscope (SEM), e.g. we can determine the crystallographic indices of cleavage planes and of directions on such planes.

For a nitrogen alloyed ferritic-austenitic duplex steel X3CrMnNiMoN 25 6 4 the crack growth resistance is recorded in terms of the J -integral, J , and the energy dissipation rate, D . Due to the anisotropic microstructure of elongated ferrite and austenite domains, very different resistance curves appear for three different crack plane orientations. Metallographic and stereophotogrammetric studies lead to a model which is able to explain these curves. It is found that the geometrical arrangement of the (brittle) ferrite and the (ductile) austenite domains is the main influence factor on the crack growth resistance (and not the volumetric fraction of ferrite and austenite). Since no standard J IC -values can be determined, a procedure is proposed to evaluate an alternative measure of the fracture initiation toughness, i.e. “quasi-initiation” J -integral values.

A numerical simulation of the stable crack growth in a thick smooth compact tension specimen with two-dimensional elastic-plastic finite element analyses is presented. The different fracture behaviors in the center and near the side surfaces of the specimen were accounted for by using plane strain analysis for the center part and plane stress analysis for the surface part. The input data to control the fracture initiation and the crack growth, i.e. CTOD i , and CTOA C , were directly measured from the center and the side surfaces of specimens. The calculated results were compared with the experimental ones. A satisfactory agreement was achieved.

A model is presented to simulate a 3D elastic-plastic FE analysis of a fracture mechanics specimen with 2D analyses. Its application for CT specimens is thoroughly investigated. It is shown that the model can easily be used and the result is very satisfactory.

International audience; The application of crystal plasticity in finite element codes provides a virtual copy of a real grain structure, including stress–strain state and slip system activity. This paper presents, first, finite element computations of an oxygen-free, high-conductivity copper multicrystal under monotonic tension. A series of polishing operations are used to reveal the real three-dimensional (3-D) microstructure, so that the mesh is a full 3-D mesh. A single crystal plasticity model is used to represent the elasto-plastic behavior for each of the approximately 100 grains. The results obtained with a full 3-D mesh and an extended 2-D mesh with columnar grains are compared in order to check the bias introduced by a simplified mesh generation. The paper goes on to compare the computational results to experimental data obtained by orientation image microscopy and local strain field measurements. Local strain and lattice rotation fields are shown. Finally, the numerical results for the slip system activity are analyzed.

The material forces concept has become an elegant tool in continuum mechanics for the calculation of the thermodynamic driving force of a defect. Based on this concept, we have recently shown that inhomogeneities essentially shield or anti-shield crack tips from applied far-field stresses. The goal of this paper is to illustrate this by considering the model example of a crack in a CT-type specimen that contains a bimaterial interface. The crack driving force is calculated as the sum of the far-field driving force and the crack-tip shielding or anti-shielding. Several cases of inhomogeneity in either thermal or elastic properties are considered. Rather simple hand calculations are provided in addition to numerical results to illustrate the advantages of using the material forces concept.