ANTIPLANE SHEAR FIELDS NEAR A CRACK-TIP IN A BRITTLE DAMAGED MATERIAL

In this paper,a simplified brittle damage model is proposed according to the Mazars-Lemaitre damage model for concrete.A closed-form solution for a mode Ⅲ crack is obtained based on the simplified model under small scale damage conditions,which allows for discontinuities of displacement-gradient and tangential stress on the damage boundary.It is pointed out that the discontinuities of field variables near the tip region exist for the brittle damaged material induced by the softening effect of the material.

Perfect elastic-viscoplastic field at mode I dynamic propagating crack-tip

The viscosity of material is considered at propagating crack-tip. Under the assumption that the artificial viscosity coefficient is in inverse proportion to power law of the plastic strain rate, an elastic-viscoplastic asymptotic analysis is carried out for moving crack-tip fields in power-hardening materials under plane-strain condition. A continuous solution is obtained containing no discontinuities. The variations of numerical solution are discussed for mode Ⅰ crack according to each parameter. It is shown that stress and strain both possess exponential singularity. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. And the tip field contains no elastic unloading zone for mode I crack. It approaches the limiting case, crack-tip is under ultra-viscose situation and energy accumulates, crack-tip begins to propagate under different compression situations.

SUPPLEMENTARY STUDY ON ANISOTROPIC PLASTIC STRESS FIELDS AT A STATIONARY PLANE-STRESS CRACK-TIP

Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.

THE ASYMPTOTIC SOLUTION TO THE ANTIPLANE SHEAR DYNAMICCRACK-TIP FIELD IN AN ELASTIC STRAIN-SOFTENING VISCOPLASTIC MATERIAL

The elastic strain softening-viscoplastic model is given in this paper. Using this model, the asymptotic stress and strain equations surrounding the tip of a propagating crock are given and numerical results ale obtained under antiplane shear. The analysis and calculation show that at the crack tip the strain possesses logarithmic singularity (ln(R/r))(1/(n+1)) while the stress is like (ln(R/r))(-n/(n+1)), therefore the asymptotic behaviour of the elastic strain-softening viscoplastic field is revealed under the antiplane shear.

ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE-STRESS CRACK-TIP

Under the condition that all the stress components at a crack-tip are the functions of 0 only, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip. Applying this general solution to four particular cases of anisotropy, the general solutions of these four particular cases are derived. Finally, we give the anisotropic plastic field at the rapidly propagating plane-stress mode I crack-tip in the case of X=Y=Z

POWER LAW NONLINEAR VISCOELASTIC CRACK-TIP FIELDS

The aim of this paper is to derive the power law type nonlinear viscoelastic crack-tip fields.For the requirement of later derivation,the HRR singular fields and the high-order asymp- totic fields are first examined.That they are essentially the isotropic,incompressible,power law type nonlinear elastic crack-tip fields is illustrated.After a concise review of the elasticity recov- ery correspondence principle for solving the nonlinear viscoelastic problems,the correspondence principle for solving the crack problems of power law type nonlinear viscoelastic materials under the first type boundary condition is proposed.The solution of the crack-tip stress,strain fields for the power law type nonlinear viscoelastic materials,especially for the modified polypropylene, is obtained.

The Plane Stress Crack-Tip Field for an Incompressible Rubber Material

The crack-tip field under plane stress condition for an incompressible rubbermaterial￣[1] is investigated by. the use of the fully nonlinear equilibrium theory. It isfound thai the crack-tip field is composed of two shrink sectors and one expansion se-ctor. At the crack-tip, stress and strain possess the singularity of R￣(-1) and R￣(-1n), respec-tively, (R is the distance to the crack-tip before deformation, n is the material const-ant). When the crack-tip is approached, the thickness of the sheet shrinks to zerowith the order of R￣(1.4n). The results obtained in this paper are consistent with that ob-tained in [8] when s→∞ .

HYDROSTATIC STRESS-DEPENDENT PERFECTLY-PLASTIC STRESS FIELDS AT A STATIONARY PLANE-STRESS CRACK-TIP

Under the condition that all the stress components at a crack-tip are the functions ofθonly,making use of equilibrium equations and hydrostatic stress-dependent yield condition,in this paper,we derive the generally analytical expressions of the hydrostatic stress-dependent perfectly-plastic stress fields at a stationary plane-stress crack-tip.Applying these generally analytical expressions to the concrete cracks,the analytical expressions of hydrostatic stress-dependent perfectly-plastic stress fields at the tips of mode I and mode II cracks are obtained.

ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING CRACK-TIP

Under the condition that all the stress components at a crack-tip are the functions of only, making use of the equations of steady-slate motion, stress-strain relations and Hill anisotropic yield conditions, we obtain the general solutions at a crack-tip in both the cases of anti-plane and in-plane strains. Applying these general solutions to the concrete cracks, the anisotropic plastic fields at the rapidly propagating tips of mode III and mode I cracks are derived.

MOLECULAR DYNAMICS SIMULATION OF CRACK-TIP PROCESSES IN COPPER

The crack tip processes in copper under mode II loading have been simulated by a molecular dynamics method. The nucleation, emission, dislocation free zone (DFZ) and pile-up of the dislocations are analyzed by using a suitable atom lattice configuration and Finnis & Sinclair potential. The simulated results show that the dislocation emitted always exhibits a dissociated fashion. The stress intensity factor for dislocation nucleation, DFZ and dissociated width of partial dislocations are strongly dependent on the loading rate. The stress distributions are in agreement with the elasticity solution before the dislocation emission, but are not in agreement after the emission. The dislocation can move at subsonic wave speed (less than the shear wave speed) or at transonic speed (greater than the shear wave speed but less than the longitudinal wave speed), but at the longitudinal wave speed the atom lattice breaks down.

EXPERIMENTAL GH SINGULARITY FIELD AROUND GROWING CRACK-TIP

The displacement fields u_x,u_y at growing crack tip of LYI2-M specimens with double edge cracks are measured using moire method.The experimental singularity fields are compared with GH theoretical field [12-14].The size and shape of the experimental GH singularity fields are obtained.The error in both the experimental and theoretical evaluations is controlled within ±10%.The experiments show that there is (In A/r)^(+1)singularity dominant around a growing crack tip.The shape of this dominant region ranges from butterfly wing to oblate and circular.Inside GH-field,there is a 3-D deformed damage zone where no GH sin- gularity exists.

Estimation of J—R Curves for Small-Sized COEC Specimens and Its Application Considering Crack-Tip Cons tr aints

The normalization method has been employed to estimate the J-resistance (J—R) curves for C-shaped outside edge-notched compression (COEC) specimens of SA-508 steel. The COEC specimens present the lowest J—R curves in comparison with other three types of specimens. Based on the J—Q—M met hod, the constraint parame ter Q determined at the mid-plane in the through-thickness direction of the specimen is used to approximately quantify the threedimensional crack-tip constraint for COEC specimens. Combining with the previous experiments on J—R curves, the constraint-coirected J—R curves for SA-508 steel specimens are given, which may be used to predict the fracture toughness of actual cracked components in structural integrity assessment.

Quantitative analysis of nanoscale deformation fields of a crack-tip in single-crystal silicon

A mode II crack in single-crystal silicon was investigated experimentally using high-resolution transmission electron microscopy.Geometric phase analysis and numerical moiré method were employed to map the deformation fields of the crack-tip area.The normal strain field maps of the crack-tip area indeed showed the deformation occurs primarily in the vicinity of the dislocations and the normal strains are near zero in the crack-tip area.The shear strain field map shows that the relatively large shear strain is in the crack-tip area.The experimental results were compared with the predictions of linear elastic fracture mechanics.The comparison shows that measured strain distribution ahead of the crack-tip agrees with the predictions of linear elastic fracture mechanics up to 1 nm from the crack-tip.

Determination of Two-Dimensional Plastic Zone Shape and SIF at Crack-Tip Using RKPM

Reproducing kernel particle Method （RKPM） is a meshless technology which has proven very useful for solving problems of elastic plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-hard ening material is obtained using RKPM. Ramberg-Osgood stress-strain relation is assumed and the crack-tip stress intensity factor （SIF） before and after formation of the plastic zone are examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility criteria are employed. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. The effects of different dilation parameters on SIF under plane-stress and plane-strain conditions are ~tudied. Results including plastic zone shape are compared with finite element method （FEM） to show the accuracy of RKPM. The main objective is to study the effects of different dilation parameters on SIF under plane stress and plane strain conditions and to obtain the mode I plastic zone shape at the crack-tip in a work hardening material using RKPM.

Higher-Order Analysis of Crack-Tip Fields in Power Law Hardening Materials

In this paper,we present an exact higher-order asymptotic analysis on the near-crack-tip fields in elastic-plastic materials under plane strain,Mode 1.A four- or five-term asymptotic series of the solutions is derived.It is found that when 1.6 < n≤2.8 (here,n is the hardening exponent),the elastic effect enters the third-order stress field; but when 2.8< n≤3.7 this effect turns to enter the fourth-order field,with the fifth-order field independent.Moreover,if n>3.7,the elasticity only affects the fields whose order is higher than 4.In this case,the fourth-order field remains independent.Our investigation also shows that as long as n is larger than 1.6,the third-order field is always not independent,whose amplitude coefficient K3 depends either on K1 or on both K1 and K2 (K1 and K2 arc the amplitude coefficients of the first- and second-order fields,respectively).Finally,good agreement is found between our results and O'Dowd and Shih's numerical ones by comparison.

Geometry independent C^(*)-T_(z) dominance of three-dimensional quasistatic growing crack-tip fields in creeping solids

In creeping solids,plane stress and plane strain solutions for asymptotic singular crack-tip fields have been first put forward by Riedel and Rice with C^(*)as the dominating parameter and developed by Xiang and Guo into three-dimensional solution(3D)for stationary cracks under the domination of C^(*)with the constraint factor Tz.However,how to characterize the 3D crack-tip fields under creep damage-induced quasistatic growing conditions remains challenging.In this study,we reveal that,for 3D quasistatic growing cracks,the leading singular solution can effectively characterize the crack-tip stress distributions with relative errors less than 10.8%for relative creep time up to 0.8 in various specimens with finite thickness.For a given relative time,Tz distributions can be unified by the equivalent thickness concept,Beq.The results show that C^(*)-T_(z) can effectively quantify both the load and constraint effects on the crack-tip fields.Such geometry independent dominance can considerably simplify the treatments of load and constraint effects,thereby promoting the application of fracture mechanics in high-temperature damage tolerance designs.

Fracture behavior dependent on crack-tip shapes in nanoscale crack-defect monolayer boron nitride sheets

Nanoscale defects,including cracks,circular holes,and the triangular-shaped defects,often occur in the growth of boron nitride nanosheets(BNNS).In this study,the fracture behavior of chiral BNNS with different crack-tip shapes and the interactions of nanoscale crack-defects are studied using molecular dynamics(MD)simulations and finite element(FE)analysis.Both MD and FE results indicate that the fracture strength of BNNS with two crack tips(t=2)is significantly higher than that with one crack tip(t=1),in which the difference in zigzag(ZZ)direction is more obvious than that in armchair(AC)direction,mainly due to the fact that the change of bond angles near the crack tips is more substantial in the ZZ direction than those in the AC direction.Our results show that the fracture strength of BNNS strongly depends on crack-tip shapes,chiral angles,the defect-to-crack tip spacing and deflection angles.Checking against the current MD simulations and FE analysis shows the present results are reasonable.This study should be of great importance for enhancing the fracture performance of BNNS by modulating their crack-tip shapes and the interactions of nanoscale crack-defects.

应变和极化协同作用下裂纹尖端阳极溶解行为

金属材料在服役过程中,其表面裂纹的尖端会因受到应力作用而优先发生局部塑性变形;加之极化的共同作用,其与裂纹以外区域在腐蚀行为和腐蚀速率方面存在明显差异。本文使用自主设计的原位加载台,与扫描振动电极技术(SVET)和电化学工作站相结合,深入研究了酸性NaCl溶液中316L不锈钢裂纹尖端在应变和极化协同作用下的阳极溶解行为。结果表明:裂纹尖端是应力集中区,应变会导致裂纹尖端的钝化膜破裂及金属局部的快速阳极溶解。当金属处于开路电位或较低阳极极化电位下时,裂纹尖端新暴露的金属表面能快速钝化,导致总电流短暂上升然后迅速下降。在较高的阳极极化电位下,即使该电位处于316L不锈钢的钝化区,新暴露的金属表面也不能再次钝化,导致裂纹尖端局部位置持续的阳极溶解。在点蚀电位以上,316L表面会发生点蚀,由于应变新暴露的金属表面也不能再次钝化,导致裂纹尖端局部位置和点蚀处均为样品表面持续的阳极溶解区。

孔洞对疲劳裂纹扩展路径的影响

为了研究孔洞位置和尺寸对疲劳裂纹扩展路径的影响,利用ABAQUS有限元仿真软件建立改进CT试样的裂纹扩展仿真模型,采用扩展有限元法研究了在低周疲劳加载条件下Q235钢圆孔与裂纹尖端的角度、距离以及圆孔半径对裂纹扩展路径的影响,并通过引入裂纹偏转系数来定量描述不同参数对裂纹扩展路径偏转程度的影响。结果表明:当圆孔与裂纹尖端的夹角为45°时,裂纹偏转系数取得最大值;裂纹偏转系数随着孔洞半径的增加逐渐增大,随着圆孔与裂纹尖端距离的增大逐渐减小。

基于HRR场的疲劳裂纹扩展模型研究

针对实际工程中安全性与经济性的需求,基于Hutchinson-Rice-Rosengren(HRR)应力-应变场提出一种Ⅰ型疲劳裂纹扩展速率预测模型。采用HRR应力-应变场描述裂纹尖端区域的应力应变分布状态,在考虑循环载荷及应变能密度理论的前提下,定义一个裂纹尖端损伤区域;同时,为消除裂纹尖端的应力奇异值问题,建立考虑裂纹尖端钝化效应的钝化半径计算方法;结合RICE的塑性叠加法与塑性应变能失效准则,发展一种Ⅰ型疲劳裂纹扩展速率模型。利用所提LIUX(HRR)预测模型对9种金属材料裂纹扩展速率进行计算,与Pandey(HRR)与CHEN-CAI Rice-Kujawski-Ellyin(RKE)两种裂纹扩展预测模型计算结果进行对比分析。同时,基于R2拟合效果及疲劳裂纹扩展三阶段的不同需求,给出三种预测模型的预测结果,并从安全性、精确性及经济性三方面给出相应的评分。最终结果表明,LIUX(HRR)预测模型适用范围更广,拟合效果更佳,能够更好地满足实际工程中的经济性与安全性的需求。