ASYMPTOTIC ANALYSIS OF PLANE-STRAIN MODE I STEADY-STATE CRACK GROWTH IN TRANSFORMATION TOUGHENINGCERAMICS(Ⅱ)

I.IntroductionThemechanismoffracturetoughnessenhancementinceramicshasbeenwidelystudiedsincetheearlyl98Os.ThepioneeringconstitutivemodeldevelopedbyBudianskyetal.ll1includestheeffectofplasticdiIation,butneglectsthetransformation-inducedshearstrain.Andtheirc…     

理想塑性介质中平面应力 静止裂纹的尖端弹塑性场

本文详细分析了理想塑性介质中平面应力I型静止裂纹的尖端弹塑性场,结果表明:裂纹尖端应力场内可以不包含应力间断线,但含有弹性区,作为这个一般解的特殊情况,当弹性区被两侧的塑性区挤压消失而尖端场成为满塑性区时,便得到Hutchinson(1968)给出的解,此外,文中还给出了另一种均匀应力区位于裂纹前方的解,这是[1]未曾得到的。     

Steady growth of cracks in compressible elastic-plastic media

Based on the theoretical framework for crack growth analysis provided by Gao and Hwang, the 5-sector solution of near-tip fields of mode-I cracks growing quasi-statically and steadily in compressible elastic perfectly plastic materials is obtained. As Poisson's ratio ν tends to 1/2, the 5-sector solution degenerates to the 4-sector solution of near-tip fields of crack growth in incompressible elastic perfectly plastic materials. The project supported by the National Natural Science Foundation of China.     

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.     

Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material

This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively.     

脆性损伤材料裂纹尖端的局部解

本文利用Mazars和Lemaitre提出的混凝土脆性损伤模型,求得了裂纹尖端应力、应变及损伤的局部解.对手Ⅲ型及不可压缩平面应变Ⅰ型裂纹,其尖端场的构造和理想塑性材料相类似.指出由于丧失了应力全连续条件,从而损伤边界不能由局部解定出.     

Fields near a rapidly propagating crack-tip in an elastic perfectly-plastic material

Dynamic effects are investigated for the steady-state fields of stress and deformation in the immediate vicinity of a rapidly propagating crack-tip in an elastic perfectly-plastic material. Both the cases of antiplane strain and in-plane strain have been considered. The governing equations in the plastic regions are hyperbolic in nature. Simple wave solutions together with uniform fields provide explicit asymptotic expressions for the stresses and the strains in the near-tip regions. The dynamic solutions describe a region of plastic loading which completely surrounds the propagating crack-tip.     

High-magnification moiré interferometer for crack tip analysis of steels

A high-magnification moiré interferometer, particularly suitable for near-tip field analysis in cracked materials, is described. It has a submillimeter field of view, a high-resolution image sensor (1.4 million pixels), X-Y-Z translation stage and an optical fiber light delivery system. These features enable the microscope head to observe the crack tip while the specimen is loaded in a standard tensile test machine. Automated fringe pattern analysis, using temporal phase shifting and spatial phase unwrapping, enables thex ory displacement component to be measured and the corresponding in-plane strain component computed. The displacement placement accuracy is better than 40 nm, and the effective strain gage dimension is ∼ 25 μm. Furthermore, the interferometer has a built-in white light microscope that allows the observation of the specimen granular microstructure in exact registration with the displacement field. The interferometer has hence been employed to investigate the near-tip fields of a precracked stainless steel specimen under load. The influence of the grain boundaries on the measured displacement fields was relatively minor. The near-tip strain field shows a significant asymmetrical behavior despite pure mode lloading conditions.     

Stable crack growth along a brittle\ductile interface—II. Small scale yielding solutions and interfacial toughness predictions

The problem of a crack growing steadily and quasi-statically along a brittle\ductile interface under plane strain, mixed mode, and small scale yielding conditions is considered. The ductile material is assumed to be characterized by the J₂-flow theory of plasticity with linear strain hardening, while the brittle material is assumed to be linear elastic. A displacement-based finite element method, exploiting the convective nature of the problem, is utilized to solve the relevant boundary value problem. In Part I of this work, the corresponding asymptotic problem was solved. This paper addresses the full-field problem in order to validate the asymptotic solutions, and to explore the physical implications of the results. The numerical full-field results are found to be in good agreement with the analytical asymptotic solutions. In particular, the full-field results strongly suggest that the stress fields in the vicinity of the crack tip are variable-separable of the power singular type; and also that the mode mix of the near-tip stress fields is, to a large extent, independent of the applied elastic mode mix. The amplitude (the plastic stress intensity factor) and the regions of validity of the asymptotic fields are estimated from the full-field results, and are observed to be strongly dependent on the applied mode mix. The remote elastic loading fields appear to influence the near-tip fields, primarily, through the plastic stress intensity factor. The present work also explores the suggestion made by Bose and Ponte Castaneda, 1992 that the solutions to the small scale yielding problem may be used in the context of a standard crack growth criterion, requiring that continued growth take place with a fixed near-tip crack opening profile, to obtain theoretical predictions for the dependence of interfacial toughness on the applied mode mix. Based on the numerical results, predictions for mixed mode toughness of the brittle\ductile interface are reported. The results, which are in qualitative agreement with available experimental data and also with some recent theoretical results, predict a strong dependence of interfacial toughness on mode mix. This suggests that ductility provides the main operating mechanism for explaining the dependence of interfacial toughness on the mode mix of the applied loading fields, during steady crack growth.     

Crack-tip fields for fast fracture of an elastic-plastic material

An asymptotic analysis of the near-tip fields is given for transient crack propagation in an elastic-plastic material. The material is characterized by J₂ flow theory together with a bilinear effective stress-strain curve. Both plane stress and plane strain conditions have been considered. Explicit results are given for the order of the crack-tip singularity, the angular position at which unloading occurs, and the angular variation of the near-tip stresses, all as functions of the crack-tip speed and the ratio of the slopes of the two portions of the bilinear stress-strain relation. It was found that the results are much more sensitive to the elastic-plastic constitutive relation than to the crack speed. This result is important for numerical analyses of dynamic crack propagation problems.