The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

Deformation of brittle materials with scattered cracking

A structural approach combined with the energy method is used to construct a continuum model of the joint process of deformation and scattered cracking in elastic-brittle isotropic materials. The proposed approach allows one to match the form of the symmetry of the effective deformation properties and damageability of the material depending on the stress state character.     

Path dependency in thermoelastic stress analysis

In this paper we review the basis of the technique for thermoelastic stress analysis and, in particular, we examine the relationship between the theory and the technique in common practice. The theory of thermoelastic stress analysis is based on the thermomechanical behavior of bodies, which takes strain and temperature as state variables that are path-independent, whereas the conventional instrumentation used in thermoelastic stress analysis involves an integration of photon flux derived from a body's surface temperature, and hence is time- and path-dependent. This inconsistency might be negligible for some, or perhaps most, applications. However, in those cases where the waveform of the loading is irregular, experiments have shown that the difference can be significant. The nature of most apparatus for thermoelastic stress analysis implies that this results is important when conducting experiments in which the forcing signal is unknown or not sinusoidal. J.R. Estrada Estrada was a Research Student and E.A. Patterson (SEM Member) was a Professor, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield, S 3JD, UK.     

Scattered fracture of porous materials with brittle skeleton

A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compressible fluid is formulated in the isothermal approximation. The model takes account of the skeleton elastic energy transformation into the surface energy of microcracks. In the case of arbitrary deformations of an anisotropic material, constitutive equations are obtained in a general form that is necessary and sufficient for the objectivity and thermodynamic consistency principles to be satisfied. We also formulate the kinetics equation ensuring that the scattered fracture dissipation is nonnegative for any loading history. For small deviations from the initial state, we propose an elastic potential which permits describing the principal characteristics of the behavior of a saturated porous medium with a brittle skeleton. We study the acoustic properties of the material under study and find their relationship with the strength criterion depending on the accumulated damage and the material current deformation. We consider the problem of scattered fracture of a saturated porous material in a neighborhood of a spherical cavity. We show that the cavity failure occurs if the Hadamard condition is violated.     

Three-dimensional ductile fracture analysis with a hybrid multiresolution approach and microtomography

A modified-JIC test on CT (compact tension) specimens of an alloy (Ti-Modified 4330 steel) was carried out. The microstructure (primary and secondary inclusions) in the fracture process zone and fracture surface are reconstructed with a microtomography technique. The zig-zag fracture profile resulting from nucleation of microvoid sheets at the secondary population of inclusions is observed. Embedding the experimentally reconstructed microstructure into the fracture process zone, the ductile fracture process occurring at different length scales within the microstructure is modeled by a hybrid multiresolution approach. In combination with the large scale simulation, detailed studies and statistical analysis show that shearing of microvoids (the secondary population of voids) determines the mixed mode zig-zag fracture profile. The deformation in the macro and micro zones along with the interaction between them affects the fracture process. The observed zig-zag fracture profile in the experiment is also reasonably captured. Simulations can provide a more detailed understanding of the mechanics of the fracture process than experiments which is beneficial in microstructure design to improve performance of alloys.     

Experimental studies on the yield behavior of ductile and brittle aluminum foams

Specimen size effects are a major cause of the unreliability of foam models in finite element codes. Here, the modified Arcan apparatus is used to investigate the biaxial yielding of ductile and brittle Al foams. This apparatus subjects a central section of a “butterfly-shaped” specimen to a uniform state of plane stress. The stresses have local maxima at the central section, thus ensuring that yielding occurs there. A yield envelope, which directly relates to the crushing process, can then be determined. Size effects are introduced when using conventional methods such as tri-axial or plate-shear tests. In such tests, averages of stress and strain are measured. These measures do not represent the actual yield event, because foam's internal structure is inhomogeneous and so is the deformation field. Strain localization and failure can occur at any weak layer of cells in the bulk. In this study, we have performed a series of biaxial tests on isotropic Alporas and anisotropic Hydro closed-cell Al foams of approximately equal densities. Alporas failed locally by a ductile phenomenon of progressive crushing of cells. It also possessed uniaxial strength asymmetry. Hydro specimens parallel and perpendicular to ‘foam rise’ were investigated. The Hydro foam developed a local, characteristic brittle crack at loads in the vicinity of the yield point. Phenomenological yield surfaces, which incorporate these features are obtained for the foams, and show dependence on both the deviatoric and hydrostatic stresses. We also provide expressions for the shear and hydrostatic strengths in terms of the uniaxial strengths. Finally, the size-independence of the yield surface is verified using the uniaxial compression of tapered specimens.     

Dynamic compression-shear response of brittle materials with specimen recovery

A new configuration for compression-shear soft-recovery experiments is presented. This technique is used to investigate various failure mechanisms during dynamic multiaxial loading of an Al₂O₃/SiC nanocomposite and TiB₂. Velocity profiles of the target surface are measured with a variable sensitivity displacement interferometer, yielding normal and transverse velocity-time histories. A dynamic shear stress of approximately 280 MPa is obtained, in the Al₂O₃/SiC nanocomposite, for an imposed axial stress of about 3.45 GPa on a 540 m thick sample. This dynamic shear stress is well below the value predicted by elastic wave propagation theory. This could be the result of stress-induced damage and inelasticity in the bulk of the sample or inelasticity on the sample surface due to frictional sliding. To gain further insight into the possible failure mechanisms, an investigation of compression-shear recovery techniques, with simultaneous trapping of longitudinal and lateral release waves, is conducted.     

Stable growth of fracture in brittle aggregate materials

Fracture of concrete is analyzed by combining the resistance curve (R-curve) approach with linearly elastic solutions for the energy release rate resulting from the quasi-static crack model of Wnuk, analogous to the D-BCS model of a stationary crack used in describing quasi-brittle fracture in metals. The R-curve, representing the crack length dependence of the energy consumed per unit fracture extension, is calculated using the concept of the energy separation rate associated with a finite crack growth steps. To simplify calculations, the tensile stress transmitted across the nonlinear zone ahead of the fracture front is assumed to be uniformly distributed over the entire nonlinear zone, even though in reality it must be a gradually declining stress resulting in strain-softening; and an infinite elastic medium loaded at infinity is assumed. These assumptions permit an easy solution with the help of Green's function for an infinite elastic medium. Application to bodies of finite size then requires assuming the nonlinear zone (fracture process zone) to be negligible with regard to specimen dimensions, crack length and ligament length. Even though this assumption is not always realistic, the end results, which are of practical importance, appear reasonable. The analysis leads to a nonlinear first-order ordinary differential equation for the R-curve, which is integrated numerically. The R-curves calculated in this manner can be closely fitted to data from previous fracture tests. Only two parameters, characterizing the initial and the final lengths of the nonlinear zone, need to be adjusted to test data.     

Cohesive zone size of microcracks in brittle materials

Consideration of cohesive microcracks in continuum micromechanics is a challenging task since a lot of applications (such as, e.g., estimation of the stiffness of a microcracked solid) require a priori knowledge of the size of the cohesive zone. The latter, however, can be determined analytically only for the special case of Barenblatt–Dugdale cracks, i.e. for cracks with spatially constant cohesive tractions. Herein, we deal with the general case of spatially non-constant cohesive tractions: Generalizing the Barenblatt–Dugdale approach, we consider that each crack is surrounded by a plane annular cohesive zone characterized by a constitutive softening law (introduced as a power law) relating the vector of cohesive tractions to the displacement discontinuity. The size of this cohesive zone is then estimated using the theorem of minimum potential energy, based on a class of kinematically admissible displacement fields.     

A model of dynamic failure in ductile materials

In this paper, a dynamic failure model in ductile materials under the action of a mean tensile stress is developed. The model proposed takes into account nucleation and growth of void as part of the failure process under dynamic loading conditions. In the evolution of porosity , work-hardening behavior and rate-dependent effects are included. Numerical simulations of aluminum, aluminum alloy and OFHC copper spallation processes are performed. The results of computation are in fair agreement with experimental results.Support of this work by the special grant No.9187004 from Natural Science Fundation of China is gratefully acknowledged     

Experimental study of microhole growth and coalescence in ductile materials

The growth and coalescence of two microholes in copper foil were studied experimentally byin situ tensile tests under a scanning electronic microscope. Two microholes of 15–35 μm in diameter were arranged in different distances and orientations. It was found that the mechanisms of microhole evolution were represented by slipping band creation, and then crack initiation and propagation along the slipping bands in ligament. The process of microhole growth and coalescence was influenced by the inter-center distance and orientation of microholes. The critical surface of microholes at coalescence is about 2–2.5 times that of the initial one. The variation of both the inter-center distance and orientation depends on the initial angle.     

Modeling dynamic brittle behavior of materials with circular flaws or pores

Compressive failure of brittle materials is driven primarily by crack growth from pre-existing flaws in the material. These flaws, such as grain boundaries, pores, preexisting cracks, inclusions and missing grains, are randomly spaced and have a range of possible shapes and sizes. The current work proposes a micromechanics-based model for compressive dynamic failure of brittle materials with circular pore flaws, which incorporates both the number density and the size distribution of flaws. Results show that the distribution of flaw sizes is very important, particularly at moderate strain rate, since analyses based solely on the mean flaw size overpredict strength. Therefore, in order to increase dynamic strength at low to moderate strain rates, it is most effective to control the presence of large flaws. At very high strain rates, however, crack growth is activated even in small flaws and therefore controlling the total number density rather than the size of the flaws is effective for increasing dynamic strength. Finally, the model shows that neglecting very small flaws in the pore population may not have significant effects on the results in many cases, suggesting that the model is a useful tool for identifying a minimum resolution required for experimental characterization of microstructure.     

Analysis of localization in brittle materials through optical techniques

This paper is devoted to the experimental analysis of strain localization in rock like specimens subjected to uniaxial compression. Two different techniques are involved in this research: stereophotogrammetry and laser speckle photography. The strain fields obtained by these techniques exhibit a homogeneous response followed by a strain localization before the peak of the load verses displacement curve. These observations allow one to choose the appropriate mechanical constitutive equations to describe the behavior of such materials.