Sufficient criterion of fracture in the case with a complex stress state and non-proportional deformation of the material in the pre-fracture zone

A general case of proportional loading with a complex stress state of the material in the pre-fracture zone, which is typical for polycrystalline solids with plastic deformation, is considered. A sufficient criterion of fracture is proposed for the case of a complex stress state with non-proportional deformation of the material in the pre-fracture zone. Critical parameters of fracture (pre-fracture zone length and load) for cracks propagating in quasi-brittle materials are obtained with the use of a modified Leonov-Panasyuk-Dugdale model. The pre-fracture zone width is determined by solving the problem of the plasticity theory in the vicinity of the crack tip. The proposed modification of the Leonov-Panasyuk-Dugdale model makes it possible to estimate the critical opening of the crack and the critical displacement of the crack flanks. Inequalities that describe different mechanisms of material fracture under proportional loading (predominantly shear fracture mechanism and fracture mechanism through cleavage) are derived.     

Computing bounds to mixed-mode stress intensity factors in elasticity

A bounding procedure combined with an effective error bound method for linear functionals of the displacements and a simple two points displacement extrapolation method is presented to compute the lower and upper bounds to the stress intensity factors in elastic fracture problems. First, the displacements of two nodes (or node pairs) on the crack edges are used to construct the linear extrapolation to obtain the stress intensity factors at the crack tip, so that stress intensity factors are explicitly expressed as linear functionals of the displacements. Then, a posteriori bounding method is utilized to compute the bounds to the stress intensity factors. Finally, the bounding procedure is verified by a mixed-mode homogenous elastic fracture problem and a bimaterial interface crack problem.     

Delamination of compressed thin layers at corners

An analysis of delamination for a thin elastic layer under compression, attached to a substrate at a corner is carried out. The analysis is performed by combining results from interface fracture mechanics and the theory of thin shells. In contrast with earlier results for delamination on a flat substrate, the present problem is not a bifurcation problem. Crack closure at sufficiently high stress levels are shown to occur. Results show a very strong dependency on fracture mechanical parameters of the angle of the corner including the range of parameters where crack closure occurs. Analytical results for the fracture mechanical properties have been obtained, and these are applied in a study of the effect of contacting crack faces. Special attention has been given to analyse conditions under which steady state propagation of buckling driven delamination takes place.     

Photoelasto-plastic studies on brittle fracture of high-polymer solids

The mechanism of brittle fracture of high-polymer solids is experimentally investigated under one-or two-dimensional stress states by a new photoelastoplastic method suggested by the author. The application of the photoelasto-plastic method on the brittle-fracture problem is based on the principle that breaking stress can be computed in brittle fracture by the measurement of the fringe orderN _B of isochromatic lines at fracture point. Bending under three-point and four-point loads, and the plane problems, some having stress concentration and others being under contacting load, are examined by using rigid polyester cast resin containing styrol as a model specimen; and, in conclusion, the brittle fracture of high-polymer solids under one- or two-dimensional stress states is decided by the constant tensile stress, whose magnitude depends only upon the material used as a model specimen, and is larger than its ultimate tensile strength. Many kinds of factors in fracture are defined, and stress-concentration factors in fracture are compared with stress-concentration factors in elasticity. A new photoelasto-plastic simple method for the determination of stress-concentration factors in elasticity is suggested by utilization of the experimental results on this brittle fracture of high-polymer solids and is examined on the perforated plane problem having finite width under tension in comparison with theoretical analysis and the experimental results by other measuring methods.     

Numerical plane stress elastic–perfectly plastic crack analysis under Tresca yield condition with comparison to Dugdale plastic strip model

A number of plane stress numerical analyses of the mode I elastoplastic fracture mechanics problem have been performed in the past using the Huber–Mises yield criterion. This study employs instead the Tresca yield condition using an incremental theory of plasticity for a stationary crack. A commercial finite element program is used to solve the opening mode of fracture problem (mode I) for a square plate containing a central crack under generalized plane stress loading conditions. A biaxial uniform tensile traction is applied to the edges of a thin plate composed of a linear elastic non-work hardening material under small strain assumptions. The finite element results are compared with the analytical predictions of the Dugdale plastic strip model for a crack in an infinite plate subject to a biaxial uniform load at infinity.     

Stress–strain and fracture behaviour of 0°/90° and plain weave ceramic matrix composites from tow multi-axial properties

A computationally economic finite-element-based multi-linear elastic orthotropic materials approach has been developed to predict the stress–strain and fracture behaviour of ceramic matrix composites with strain-induced damage. The finite element analysis utilises a solid element to represent a homogenised orthotropic medium of a heterogeneous uni-directional tow. The non-linear multi-axial stress–strain behaviour has been discretised to multi-linear elastic curves, which have been implemented by a user defined subroutine or UMAT in the commercial finite element package, ABAQUS. The model has been used to study the performance of two CMC composites: a SiC (Nicalon) fibre/calcium aluminosilicate (CAS) matrix 0°/90° cross-ply laminate Nicalon/CAS; and, a carbon fibre/carbon matrix–SiC matrix (C/C–SiC) plain weave laminate DLR-XT. The global stress–strain curves with catastrophic fracture behaviour and effects of fibre waviness have been predicted. Comparisons have been made between the predictions and experimental data for both materials. The predicted results when fibre waviness is taken into account compare well with the experimental data.     

Cylindrical interface crack in a hollow layered functionally graded cylinder under static torsion

A hollow functionally graded composite cylinder under static torsion, which consists of an inner and outer elastic circular tube with a cylindrical interface crack, is studied in this work. By utilizing Fourier integral transform method, the mixed boundary value problem is reduced to a Cauchy singular integral equation, from which the numerical results of the stress intensity factor are obtained by the Lobatto–Chebyshev quadrature technique. Numerical results demonstrate the coupled effects of geometrical, physical, and functionally graded parameters on the interfacial fracture behavior.     

Deformation and fracture of crystalline materials under complex loading-program conditions

In predicting the deformation and conditions of fracture of materials under complex loading program conditions one must consider the entire duration of the deformation process.The problem becomes complicated in cases of a simultaneous operation of various mechanisms of deformation and fracture, e. g., when plastic deformation is superposed (once or repeatedly) on creep.A promising phenomenological approach to this problem may be based on concepts of the mechanical equation of state of materials. A hypothesis of the existence of the equation of state depending on a finite number of structural parameters was formulated by Kröner [1] for the case of the three-dimensional law of plasticity and by Rabotnov [2] for the case of creep and fracture under uniaxial stress state conditions.This article is concerned with the application of the hypothesis of the mechanical equation of state to the problem of deformation and fracture of materials (in the uniaxial case) under complex loading program conditions.     

The effects of void cluster size on ductile fracture

The effects of void clustering on ductile fracture are studied by modeling a discrete set of randomly distributed clusters. Each cluster consists of four, equally-spaced, cylindrical voids. The spacing between the clusters is held constant while the spacing between the voids is varied. A Eulerian finite element program is used to numerically solve the boundary value problems. A salient feature of the previous investigations is that both the ultimate stress and the fracture strain are functions of the void distribution. In contrast, the ultimate stress remains constant while the fracture strain changes with the void cluster diameter in the current investigation.     

Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic composites

Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic–matrix composites have not been satisfactorily explained by existing mechanics-based models. In this paper, we use an exact model of fiber fragmentation under global load sharing conditions to predict fracture in three model problems in which non-uniform strains occur: (i) an end-constrained plate subject to a linear transverse temperature gradient; (ii) an internally-pressurized cylindrical tube with a linear through-thickness temperature gradient; and (iii) a rectangular beam under combined bending and tension. Fracture is assumed to occur when the global load reaches a maximum value. Approximations to the exact fragmentation model are also assessed, with the goal of decoupling the effects of two important parts of the computed stress–strain response: the rate of post-peak strain softening and the magnitude of the plateau “flow” stress once fiber fragmentation is complete. We find that for cases in which the fiber Weibull modulus is low and hence its plateau strength is high relative to its peak and the loading yields a sufficiently high strain gradient, the failure strain lies in the plateau regime. Consequently, the results can be predicted with good accuracy using a perfectly-plastic representation of the post-peak response. In contrast, for cases in which the fiber Weibull modulus is high, the failure strain lies in the softening portion of the curve. Here a linear-softening model is found to yield accurate results. A preliminary assessment of the model has been made by comparing predicted and measured bending/tension strength and failure strain ratios for one specific composite. The correlations appear good, though additional experiments are required in order to critically assess the model predictions over a range of loading scenarios.     

Dynamic interfacial crack propagation in elastic–piezoelectric bi-materials subjected to uniformly distributed loading

In transversely isotropic elastic solids, there is no surface wave for anti-plane deformation. However, for certain orientations of piezoelectric materials, a surface wave propagating along the free surface (interface) will occur and is called the Bleustein–Gulyaev (Maerfeld–Tournois) wave. The existence of the surface wave strongly influences the crack propagation event. The nature of anti-plane dynamic fracture in piezoelectric materials is fundamentally different from that in purely elastic solids. Piezoelectric surface wave phenomena are clearly seen to be critical to the behavior of the moving crack. In this paper, the problem of dynamic interfacial crack propagation in elastic–piezoelectric bi-materials subjected to uniformly distributed dynamic anti-plane loadings on crack faces is studied. Four situations for different combination of shear wave velocity and the existence of MT surface wave are discussed to completely analyze this problem. The mixed boundary value problem is solved by transform methods together with the Wiener–Hopf and Cagniard–de Hoop techniques. The analytical results of the transient full-field solutions and the dynamic stress intensity factor for the interfacial crack propagation problem are obtained in explicit forms. The numerical results based on analytical solutions are evaluated and are discussed in detail.     

A comparison of cohesive zone modeling and classical fracture mechanics based on near tip stress field

A mode III crack with a cohesive zone in a power-law hardening material is studied under small scale yielding conditions. The cohesive law follows a softening path with the peak traction at the start of separation process. The stress and strain fields in the plastic zone, and the cohesive traction and separation displacement in the cohesive zone are obtained. The results show that for a modest hardening material (with a hardening exponent N = 0.3), the stress distribution in a large portion of the plastic zone is significantly altered with the introduction of the cohesive zone if the peak cohesive traction is less than two times yield stress, which implies the disparity in terms of the fracture prediction between the classical approach of elastic–plastic fracture mechanics and the cohesive zone approach. The stress distributions with and without the cohesive zone converge when the peak cohesive traction becomes infinitely large. A qualitative study on the equivalency between the cohesive zone approach and the classical linear elastic fracture mechanics indicates that smaller cracks require a higher peak cohesive traction than that for longer cracks if similar fracture initiations are to be predicted by the two approaches.     

Theoretical modeling and analysis of thermal fracture of semi-infinite functionally graded materials with edge cracks

The present investigation is devoted to a problem of the interaction of two edge cracks inclined arbitrary to the boundary of a non-homogeneous half-plane, which is a functionally graded layer on a homogeneous substrate. The functionally graded properties vary exponentially in thickness direction. One cycle of cooling from sintering temperature is considered. An approach based on integral equations is used and a solution is obtained, then the stress intensity factors are calculated and direction of the initial crack propagation is evaluated by using the maximum circumferential stress criterion. Influence of geometrical and material (inhomogeneity) parameters on the fracture characteristics is investigated. This study can serve as a part of the modeling of the fracture process in FGM coatings under cyclic heating–cooling thermal loading.     

A void–crack nucleation model for ductile metals

A phenomenological void–crack nucleation model for ductile metals with secondphases is described which is motivated from fracture mechanics and microscale physicalobservations. The void–crack nucleation model is a function of the fracture toughness of theaggregate material, length scale parameter (taken to be the average size of the second phaseparticles in the examples shown in this writing) , the volume fraction of the second phase, strainlevel, and stress state. These parameters are varied to explore their effects upon the nucleationand damage rates. Examples of correlating the void–crack nucleation model to tension data in theliterature illustrate the utility of the model for several ductile metals. Furthermore, compression,tension, and torsion experiments on a cast Al–Si–Mg alloy were conducted to determinevoid–crack nucleation rates under different loading conditions. The nucleation model was thencorrelated to the cast Al–Si–Mg data as well.     

On the stress monitoring problem for parallel gallery regions

We consider the problem of estimating the stress–strain state in underground hard mineral mines where long parallel underground galleries are formed. There are a number of papers dealing with local causes of gallery accidents due to variations in the medium stress–strain state occurring as the minerals are withdrawn. At the same time, the authors’ theory of hidden effects shows that gallery fracture can be caused both by local actions on the defect region and by some long-range factors that can affect these defects remotely by localizing the stress–strain state in the defect region. It should be noted that the stress in the gallery region is redistributed each time a new gallery is formed or the dimensions of the existing galleries are changed. In this paper, a theory for estimating the stress-strain state in underground mines with arbitrarily many parallel galleries of various dimensions is developed.It is shown that the stresses due to remote factors can be monitored in all gallery regions. The study is based on factorization methods, the block element method, and the topological approach.     

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A₂ three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A₂ approach.     

Tension–torsion fracture experiments – Part II: Simulations with the extended Gurson model and a ductile fracture criterion based on plastic strain

An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing.