Plane strain compression of aluminium alloy sheets

The theory of plane strain compression is applied to rolled aluminium alloy sheet. Two contrasting grades of the alloy are tested: naturally aged AC 120 and half-hard HE 30. While AC 120 displays a smooth stress–strain curve under homogenous straining, HE30 shows a serrated stress–strain curve due to its banded plastic strain behaviour. It is shown that, provided the r-values can be established reliably to characterise each sheet’s orthotropy, a flow curve to large strain (≃2) is provided by the plane strain test. Certain modifications to the original test procedure are made to achieve this. Equivalence in flow curves, as required of orthotropic plasticity theory, is examined from plane strain, bulge forming and tension tests conducted at various orientations to the roll. Despite the contrasting limiting strains between the three tests (tension ≃ 0.1, bulge forming ≃ 0.8) an acceptable correlation has been found between their equivalent flow curves across three decades of strain. The dependence of equivalent plastic strain upon equivalent stress for each material conforms to the Hollomon law. The Ramberg–Osgood law allows for the addition of elastic strain.     

Plane strain crack closure and cyclic hardening

This study is focused on the understanding of the mechanical effects of cyclic hardening on crack tip plasticity and on plasticity-induced crack closure. Various finite element analyses were conducted using abaqus. Cyclic hardening is found to affect both crack closure and the shape of the plastic zone at the crack tip. Crack growth modelling in plane strain conditions in a cyclically hardening material is discussed. An empirical formula is provided which allows the calculation of the crack tip plastic zone size under plane strain conditions in a cyclically hardening material. The effects of overloads are also examined.     

Plane strain crack instability under small-scale yielding conditions

A theoretical analysis shows that if a plane strain crack becomes unstable under small-scale yielding conditions after only a very small increment of stable crack extension, there being no change in fracture mode, then the difference between the crack tip stress intensity factors for the onset of crack extension and instability is also small. Implications of this prediction are discussed in relation to the fracture toughness testing of materials.     

High-temperature fatigue crack growth in Inconel 718 subjected to high strain amplitudes

Fatigue crack growth experiments in Inconel 718 subjected to high strain amplitudes at 650 °C have been conducted. In the study the effects of load amplitude, ratio and frequency have been investigated. It was found that crack growth is a mixture of cyclic and time dependent mechanisms, depending on the load frequency. The load frequency was also found to have a strong influence on the crack growth rate. Also, crack closure was found to play an important role. By using an effective J‐integral and including a frequency compensation term it was possible to summarize crack growth data into an empirical life prediction law, which seems to be in reasonable agreement with data from other studies.     

Large strain field near an interface crack tip

In this paper the elastostatic field near the tip of an interface crack between two materials is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field are derived and solved. The singular characters of stress and strain near the crack tip are revealed. The crack opening shape is discussed for various cases. It is shown that when large deformation is taken into account the oscillatory singularity does not occur.     

On the influence of laminate stacking on buckling of composite cylindrical shells subjected to axial compression

The buckling loads of laminated cylinders can strongly depend on the position of the differently oriented layers within the shell. This paper deals with two different laminated orthotropic cylinders with opposite stacking sequence of the laminate layers. Cylinders of this construction had been thoroughly tested within a BRITE EURAM project. Analytical and semi-analytical methods have been used to predict the buckling loads, and the results are reported in this paper as well as test results for comparison. An explanation of the striking influence of stacking sequence is given. With some more examples the findings are verified. It is suggested that the presented results can be used for benchmarking purpose.     

Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source

The interaction between internal defects and an interface crack in a bimaterial subjected to a thermal load, in particular a heat source, is examined. Attention is focused on the construction of the associated integral equations.     

Thermal crack problems for a bimaterial with an interface crack and internal defects subjected to a heat source

The interaction between internal defects and an interface crack in a bimaterial subjected to a thermal load, in particular a heat source, is examined. Attention is focused on the construction of the associated integral equations.     

Plane strain crack problems for elastic materials with variable properties

Distributions of stress, strain and displacement occurring at the tip of a crack in a material with properties dependent on the type of loading are investigated for the conditions of plane strain in both far-field tensile and shear loads. The causes of the dependence of material properties on the type of external forces are the various inhomogeneities such as microcracks, pores, inclusions or reinforcing components in a material. The behaviour of these inhomogeneities depends substantially on the conditions of loading or deformation. Hence, the deformation properties of a material are not fixed intrinsic material characteristics that are invariant to the loading conditions, but rather the macroproperties of such materials are stress-state-dependent ones, and this effect becomes more noticeable as the volume content of the inhomogeneities increases. The asymptotic solutions of crack problems are obtained on the basis of proposed stress-strain relations describing not only the stress-state dependence of material properties, but the interrelation between the characteristics of volume and shear deformation as well. In a non-uniform stress state the primary macrohomogeneous material becomes an heterogeneous one. The use of the stress function is not effective for the solution of plane strain crack problems for the materials under consideration. Therefore, an approach based on the corresponding representation for the strains is used. It is shown that the commonly used suppositions of the symmetry or anti-symmetry in the stress distribution relative to the crack plane can not be accepted, since they do not allow all the boundary conditions to be satisfied. The opening of the crack surfaces in the case of far shear field is observed. The influence of stress-state sensitivity of material properties on the values of the stress intensity factor is more significant for tensile crack than for the crack in far shear field.     

Plane strain crack problems for elastic materials with variable properties

Distributions of stress, strain and displacement occurring at the tip of a crack in a material with properties dependent on the type of loading are investigated for the conditions of plane strain in both far-field tensile and shear loads. The causes of the dependence of material properties on the type of external forces are the various inhomogeneities such as microcracks, pores, inclusions or reinforcing components in a material. The behaviour of these inhomogeneities depends substantially on the conditions of loading or deformation. Hence, the deformation properties of a material are not fixed intrinsic material characteristics that are invariant to the loading conditions, but rather the macroproperties of such materials are stress-state-dependent ones, and this effect becomes more noticeable as the volume content of the inhomogeneities increases. The asymptotic solutions of crack problems are obtained on the basis of proposed stress-strain relations describing not only the stress-state dependence of material properties, but the interrelation between the characteristics of volume and shear deformation as well. In a non-uniform stress state the primary macrohomogeneous material becomes an heterogeneous one. The use of the stress function is not effective for the solution of plane strain crack problems for the materials under consideration. Therefore, an approach based on the corresponding representation for the strains is used. It is shown that the commonly used suppositions of the symmetry or anti-symmetry in the stress distribution relative to the crack plane can not be accepted, since they do not allow all the boundary conditions to be satisfied. The opening of the crack surfaces in the case of far shear field is observed. The influence of stress-state sensitivity of material properties on the values of the stress intensity factor is more significant for tensile crack than for the crack in far shear field.     

Initiation, propagation and arrest of an interface crack subjected to controlled stress wave loading

An experimental study has been conducted to investigate the initiation, propagation, and arrest of bimaterial interface cracks subjected to controlled stress wave loading in the form of a tensile dilatational stress wave pulse. The tensile pulse is generated by detonating lead azide explosive in a specially designed specimen. Dynamic loading of the bimaterial interface results in crack initiation, propagation, and arrest, all in the same experiment. This failure event is observed using photoelasticity in conjunction with high speed photography. Full field data from the experimentally obtained isochromatic fringe patterns is analyzed to determine time histories of various fracture parameters such as the crack tip speed, the dynamic complex stress intensity factor, the energy release rate, and the mixity. The experimental data is also used to quantify the values of the dynamic initiation and arrest toughness and to evaluate a recently proposed dynamic interface fracture criterion. This revised version was published online in August 2006 with corrections to the Cover Date.     

Local buckling of the elastic and viscoelastic coating around the penny-shaped interface crack

In the framework of the piecewise-homogeneous body model with the use of the three-dimensional geometrically non-linear exact equations of the theory of elasticity and viscoelasticity the local buckling (delamination) problem of the elastic and viscoelastic coating around a penny-shaped interface microcrack is studied. The method of solution of the considered problem is developed with the use of boundary form perturbation method, FEM and Laplace transform. All investigations are made on the sandwich circular plate and it is assumed that interface crack edges have an insignificant initial rotationally symmetric imperfection and as a buckling criterion the case where this imperfection starts to increase and grows indefinitely is taken. Numerical results illustrating the influence of the mechanical and geometrical parameters to the critical force for elastic coating and to the critical time for the viscoelastic coating are presented.     

Shear coupling effects on stress and strain distributions in wood subjected to transverse compression

The mechanical behaviour of a wood board subjected to transverse compression is relevant to the performance of glulam beams and solid wood structures. The wood material can be described as polar orthotropic, due to the annual ring structure and to the differences in moduli in different directions in the radial–tangential plane. Strain measurements are performed on single wood boards using a whole-field digital speckle photography technique. Finite element analysis is performed and compared with experimental data. Good agreement in terms of strain fields and apparent moduli is observed between predictions and data. The experimental data show strong variations in local strain due to the polar orthotropic behaviour of wood in this plane, and the extremely low value for shear modulus G_rt as compared with the other moduli. This leads to shear coupling effects resulting in large local shear deformation and correspondingly low effective stiffness under transverse global loading.     

Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model

The beam lattice-type models, such as the Euler–Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr–Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.     

Fatigue crack propagation in Ti–6Al–4V subjected to high strain amplitudes

Fatigue crack propagation in circular Ti–6Al–4V specimens subjected to high strain amplitudes has been investigated. Crack closure was measured with an electrical potential‐drop technique. Closure was shown not to depend on strain ratio but to be a function of the applied strain range. At higher strain ranges, the crack was found to be closed for a smaller part of the load cycle than at lower strain ranges due to blunting of the crack tip. Furthermore, the use of a strain‐intensity approach to predict crack‐propagation rate was investigated, and it was found that for the upper parts of the da/dN curves the effective strain intensity yields good predictions. Also, the effective stress‐intensity factor was found to collapse the da/dN curves for different load ratios.     

Fatigue life and crack closure in specimens subjected to variable amplitude loads under plane strain conditions

The propagation of fatigue cracks in specimens subjected to variable amplitude loading under plane strain conditions was investigated experimentally and numerically, to find the influence of the variable amplitude loading on the stabilised crack closure level. Experiments on four-point-bend specimens with a Gurney block load scheme, showed that the crack closure level depends on the crack length but not on the stress range of the fluctuations. Numerical simulations performed in the fatigue crack growth program FASTRAN-II showed good agreement with the experimental results. In addition, statistical uncertainty analyses performed on the fatigue life show that, for technical applications, the uncertainties in initial crack length and load levels have a greater influence on the uncertainty in fatigue life, than the fluctuation level of the load.     

Plane stress near-tip field analysis of steady-state crack growth along a linear-hardening elastic-plastic interface

Summary In this work the asymptotic near-tip stress and velocity fields of a crack propagating steadily and quasi-statically along a ductile interface are presented for plane stress cases. The elastic-plastic materials are characterized by the J₂-flow theory with linear plastic hardening. The solutions are assumed to be of variable-separable form with a power singularity in the radial distance to the crack tip. It is found that two distinct solutions exist with slightly different singularity strengths and very different mixities on the interface ahead of the crack tip. One of the solutions corresponds to a tensile-like mode and the other corresponds to a shear-like mode. An interface will change the near-tip fild of the tensile solution obviously, whereas the shear-like solution maintains its original structure as in homogeneous materials. In cases the elastic bimaterial parameter differs from zero, the two solutions can coalesce at some high strain-hardening. An interface between two high strain-hardening materials only slightly affects the stress and velocity distribution around the tip, whereas the singularity strength deviates from the homogeneous solutions. The strength of the singularity is predominantly determined by the smaller strain-hardening material. Poisson's ratio affects variation of the singularity as a function of strain-hardening slightly if the coalescing point of the variable-separable solution is not approached. Only for the very distinct elastic moduli the near-tip field approaches the rigid interface solution.     

Failure analysis of CFRP laminates subjected to compression after impact: FE simulation using discrete interface elements

This paper presents a model for the numerical simulation of impact damage, permanent indentation and compression after impact (CAI) in CFRP laminates. The same model is used for the formation of damage developing during both low-velocity/low-energy impact tests and CAI tests. The different impact and CAI elementary damage types are taken into account, i.e. matrix cracking, fiber failure and interface delamination. Experimental tests and model results are compared, and this comparison is used to highlight the laminate failure scenario during residual compression tests. Finally, the impact energy effect on the residual strength is evaluated and compared to experimental results.     

Dynamic pulse buckling of composite shells subjected to external blast

Dynamic pulse buckling of woven E-Glass/Vinyl Ester and laminated E-Glass/Epoxy cylindrical shells subjected to uniform overpressure and asymmetric pressure pulse (side-on explosion) were examined. The solutions for the radial shell deformations were represented by Mathieu differential equations. The dynamic instability of the shells was determined from a Mathieu stability diagram. It was found that the stability of the shells depended on lay-up, aspect ratio as well as impulse distribution. The stable vibration response of the shells with side-on explosion compared well with finite element solutions using a Dynamic, Implicit analysis in ABAQUS Standard. First-ply failure of the woven E-Glass/Vinyl Ester shell with side-on explosion was predicted using a modified Hashin–Rotem failure criterion. It was shown that the thinner woven E-Glass/Vinyl Ester shells were more likely to fail by dynamic instability, whereas the thicker woven E-Glass/Vinyl Ester shells were more likely to fail by first-ply failure.