Experimental analysis of crack tip fields in rubber materials under large deformation

A three-nested-deformation model is proposed to describe crack-tip fields in rubber-like materials with large deformation.The model is inspired by the distribution of the measured in-plane and out-of-plane deformation.The inplane displacement of crack-tip fields under both Mode I and mixed-mode(Mode I-II) fracture conditions is measured by using the digital Moire’ method.The deformation characteristics and experimental sector division mode are investigated by comparing the measured displacement fields under different fracture modes.The out-of-plane displacement field near the crack tip is measured using the three-dimensional digital speckle correlation method.     

On the deformation and fracture of porous materials

The constitutive behavior of porous materials (including the yield loci, the void growth rate, the macro stress-strain relation and the strain to localization instability) is examined based on the lower bound approach proposed by the present authors. These results are then compared with the experimental and the finite element results as well as those predicted by Gurson's equations. Emphasis is placed on approaching the real behavior from the upper and the lower bound analysis. Calculation is also made on the influence of void nucleation on the critical strain to instability and a modified strain-controlled nucleation criterion is proposed. Finally the instability and fracture of AISI4340 steel in plane strain tension is examined and comparison is made between theoretical and experimental results.     

Analysis on the cohesive stress at half infinite crack tip

The nonlinear fracture behavior of quasi-brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi-brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function . The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are give     

The crack tip fields of orthotropic composite plate under bending

1MechhacalModelThefractUreproblemwhichisthesameasthatinpaper[I]isfurtherdiscussedinthispaper.TheanalysisoffractUrebehavioursnearcracktipforinfinitelinearelasticorthotropiccompositeplatewithacentralthroughcrackoflengthZaiscarriedout.ThegeometryandloadingcondihonsareshowninFig.1.Tosolvesuchaproblem,weneedtosolvethepanaldifferentialequationwiththefollowingboundaryconditions:wherewisdeflectionofcoddleplane;M.andM,arebendingmoment,Ma.istwistingmoment,andstiffnessmatrixFromthetheoryofplateL'],w…     

Higher-order crack tip fields for functionally graded material plate with transverse shear deformation

The crack tip fields are investigated for a cracked functionally graded material (FGM) plate by Reissner’s linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson’s ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner’s plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner’s effect when the in-homogeneity parameter approaches zero.     

Effect of grain size on slow fatigue crack propagation and plastic deformation near crack tip

Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δk_th increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio for different grain sizes are different at the threshold. The maximum stress intensity factor is k_max and σ_ys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10^—8 to 10⁻⁷ mm/cycle.A dimensionless relation of the form for collating fatigue crack starting growth data is proposed in which Δk_th represents the stress intensity factor range at the threshold. Based on experimental results, this relation attains the value of 0.6 for a fatigue crack to start growth in the Austenitic stainless steel investigated in this work. Metallurgical examinations were also carried out to show a transgranular shear mode of cyclic cleavage and plastic shear.     

Edge dislocations generated from blunt crack tip in viscoelastic material under residual stress

The 2D model of edge dislocations generation from blunt crack tip in viscoelastic material under residual stress has been proposed, the solution of stress field and displacement field are solved by using complex potential method, conformal mapping and Laplace inverse transformation. The explicit expressions of stress intensity factor, strain energy density and crack tip slide displacement are obtained in closed form. The principle of compatibility of blunt crack to edge dislocations has been used to evaluate the dislocations number and dimensionless ratio α. Numerical results present that the number of edge dislocations first increases and then decreases with increase of zone size ratio of the dislocations zone and none-dislocations zone, but it can be reduced by higher configurations ratio of semi-minor axis and semi-major axis. In addition, it increases with time and tends to be a constant quickly. The normalized multiplier α first increases and then decreases with increase of zone size ratio. In addition, it decreases with time and the increase of crack configurations ratio. Both normalized micro-volume SED and normalized dislocation-volume SED decrease with increase of distance from crack tip and tend to vanish. But the dislocation-volume SED decreases more quickly than micro-volume SED does, because of its stronger singularity. Moreover, they increase with time and decrease of configurations ratio.     

On perfectly stress field at a mixed-mode crack tip under plane and anti-plane strain

In [1], under the condition that all the perfectly plastic stress components at a crack tip are functions of ϕ only, making use of equilibrium equations, stress-strain rate relations, compatibility equations and yield condition. Lin derived the general analytical expressions of the perfectly plastic stress field at a mixed-mode crack tip under plane and anti-plane strain. But in [1] there were several restrictions on the proportionality factor γ in the stress-strain rate relations, such as supposing that γ is independent of ϕ and supposing that γ=c or cr⁻¹. In this paper, we abolish these restrictions. The cases in [1], γ=cr^d (n=0 or-1) are the special cases of this paper.     

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK _I , the crack tip biaxiality parameter is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK _I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK _I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.     

Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation

The three-dimensional field equations can in general be regarded as the sum of in-plane and out-of-plane deformation. The method for the general solution is the same for both although the boundary conditions could make a difference. If a particular solution in exact form may be found for the out-of-plane case, the same may not hold for the in-plane case. Hence, there may be a good reason for discussing the out-of-plane crack problem in certain situations that should be emphasized. Otherwise, the reason may lie in the exploration of possible application to the in-plane problem, a direct solution of which would have required a considerable effort. The contribution of this work rests on the new findings for the case of poling parallel to the crack in a magnetoelectroelastic composite made of BaTiO₃–CoFe₂O₄. The inclusions are BaTiO₃ and the matrix is CoFe₂O₄. Several new features of the solution were not expected before hand.Unlike in-plane deformation with poling normal to the crack plane, maximum crack growth enhancement is found to occur in the BaTiO₃–CoFe₂O₄ composite for a volume fraction of about 50%. Crack retardation increases as the volume fraction of the inclusions either increase or decrease. The occurrence of this same phenomenon in Mode I and II remain to be investigated. Poling direction of magnetic and electric field for line defects can have a significant effect on crack growth for magnetoelectroelastic materials. The foregoing conclusions are based on predictions made from the strain energy density criterion.     

Harmonic vibrations of a half-space with a surface-breaking crack under conditions of out-of-plane deformation

The paper presents a solution of the problem of determining the stress state in an elastic isotropic half-space with a crack intersecting its boundary under harmonic longitudinal shear vibrations. The vibrations are excited by a regular action of a harmonic shear load on the crack shores. The solution method is based on the use of the discontinuous solution of the Helmholtz equation, which allows one to reduce the original problem to a singular integro-differential equation for the unknown jump of the displacement on the crack surface. The solution of this equation is complicated by the existence of a fixed singularity of its kernel. Therefore, one of the main results is the development of an efficient approximate method for solving such equations, which takes into account the true asymptotics of the unknown function. The latter allows one to obtain a high-precision approximate formula for calculating the stress intensity factor.     

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     

A finite element study of the near crack tip deformation of a ductile material under mixed mode loading

In ductile fracture, voids near a crack tip play an important role. From this point of view, a large deformation finite element analysis has been made to study the deformation, stress and strain, and void ratio near the crack tip under mixed mode plane strain loading conditions, employing Gurson's constitutive equation which has taken into account the effects of void nucleation and growth. The results show that: (i) one corner of the crack tip sharpens while the other corner blunts, (ii) the stress and strain distributions except for the near crack tip region, can be superimposed by normalizing distance from the crack tip by a crack tip deformation length, i.e., a steady-state solution under a mixed mode condition has been obtained, (iii) the field near a crack tip can be divided into four characteristic fields (K field, HRR field, blunted crack tip field, and damaged region), and (iv) the strain and void volume fraction become concentrated in the sharpened part of a crack tip with increasing Mode II component.     

A crack emanating from the tip of bonded dissimilar materials

1.IntroductionBondedstructurescanbewidelyfoundindifferentareas,suchasweldedpressurevessels,reinforcedconcretemembers,groutingsoftfoundationandsolidrocketpropellants.etc.Thestudy'ofthesingularityofbondedstructuresisespeciallyimp6rtantnotonlyforsafedesignbutalsoforconstruction.DeinpseyandSinclairl61studiedthegeneraleaseofN-materialcompositewedges,andprovedthat'ingeneralthereexistsstresssingularitynearthetipofthewedges,andtheorderofthesingularitydependsontheelasticconstantsandthelocalgeometry.Fo…     

An experimental study of the deformation fields around a propagating crack tip

Digital image processing was used to obtain the deformation fields around a propagating crack tip from photographic films recorded by a high-speed Cranz-Schardin camera. The in-plane displacements and strains determined from the process were then used to compute the dynamic stress intensity factor and the remote stress component parallel to the crack face.K dominance is discussed using the experimental data. Surface roughness of the fractured surface is also examined.     

高韦伯数条件下黏性对液滴变形过程的影响

为探究液滴黏性对变形过程的影响,深入了解液滴在冲击波作用下变形破碎的行为机制。采用高速阴影技术在水平激波管上拍摄了高韦伯数（We=1 100～4 400）条件下,3种黏性硅油液滴的变形过程。结果表明随着黏性的提升：液滴演化出相应特征所需时间增大,同时会出现新的变形特征;液滴空间及位移特征参数的生长速率降低而变形时间、最大变形高度/位移都增大,这是因为提升的黏性力降低了变形速率、耗散了更多的动能并延长了液滴的变形过程;液滴表面最不稳定的Kelvin-Helmholtz波朝着大尺度、低生长率的方向发展,从而实现黏性对变形过程的延缓作用。随着最大变形位移的增大,最大变形高度首先线性增长,之后增幅降低。

     

Axially symmetric thermal stress of an external circular crack under general thermal conditions

Summary The paper presents a solution for the linear thermoelastic problem of determining axisymmetric stress and displacement fields in an isotropic elastic solid of infinite extent weakened by an external circular crack under general mechanical loadings and general thermal conditions. The mechanical loadings and thermal conditions applied on the crack faces are axisymmetric, being non-symmetric about the crack plane. In similar lines of [7], equations of equilibrium of an elastic solid conducting heat have been solved using Hankel transforms and Abel operators of the first kind. Expressions for stress, displacement, temperature and heat flux functions are obtained in terms of Abel transforms of the first kind of the jumps of stress, displacement, temperature and heat flux at the crack plane. Two types of thermal conditions, that is, general surface temperatures and general heat flux on faces of the crack are considered. In both the cases, closed form solutions have been obtained for the unknown functions solving Abel type of integral equations. Explicit expressions for stresses, displacements, temperature fields, stress intensity factors have been obtained. Two special cases of thermal conditions in which: (i) crack faces are subjected to constant non-symmetric temperatures over a circular ring area, (ii) crack faces are subjected to constant non-symmetric heat flux over a circular ring area, have been considered. In some special cases, results have been compared with those from the literature.     

高应变率大变形下的聚丙烯/尼龙共混高聚物损伤型本构特性

对两种采用不同相容剂的聚丙烯（PP）和尼龙（PA）共混高聚物材料在大变形下的粘弹性力学行为进行研究,着重考察应变率效应和损伤的演化,从而分析不同的界面分子设计对共混体系材料宏观性能的作用。在准静态及冲击实验研究的基础上,基于ZWT非线性粘弹性模型,并结合了遗传算法,分别得到了能有效描述两种共混高聚物大变形阶段计及损伤的非线性粘弹性本构关系。两种材料在不同加载条件下表现出明显不一致的性能,原因在于其损伤演化的率相关性,且两种材料的大变形机制存在一定的差别,能用ZWT方程进行描述的范围也不一样。     

A Peierls criterion for the onset of deformation twinning at a crack tip

A criterion for the onset of deformation twinning (DT) is derived within the Peierls framework for dislocation emission from a crack tip due to Rice (J. Mech. Phys. Solids 40(2) (1992) 239). The critical stress intensity factor (SIF) is obtained for nucleation of a two-layer microtwin, which is taken to be a precursor to DT. The nucleation of the microtwin is controlled by the unstable twinning energyγ_ut, a new material parameter identified in the analysis. γ_ut plays the same role for DT as γ_us, the unstable stacking energy introduced by Rice, plays for dislocation emission. The competition between dislocation emission and DT at the crack tip is quantified by the twinning tendencyT defined as the ratio of the critical SIFs for dislocation nucleation and microtwin formation. DT is predicted when T>1 and dislocation emission when T<1. For the case where the external loading is proportional to a single load parameter, T is proportional to . The predictions of the criterion are compared with atomistic simulations for aluminum of Hai and Tadmor (Acta Mater. 51 (2003) 117) for a number of different crack configurations and loading modes. The criterion is found to be qualitatively exact for all cases, predicting the correct deformation mode and activated slip system. Quantitatively, the accuracy of the predicted nucleation loads varies from 5% to 56%. The sources of error are known and may be reduced by appropriate extensions to the model.