三维疲劳弹塑性弯曲裂纹塑性区研究

主要研究疲劳载荷作用下的三维弹塑性弯曲裂纹尖端的塑性区问题.用数值解法计算出三维弹塑性弯曲裂纹尖端交变塑性区于裂纹直线部分延长线上的投影长度的最大值和变化幅值,作图分析了三维弹塑性弯曲裂纹尖端交变塑性区尺寸的最大值和变化幅值与三维裂纹体几何尺寸之间的关系.三维弹塑性弯曲裂纹尖端交变塑性区的最大值和变化幅值随着三维裂纹体厚度的增大而减小,随着三维裂纹体厚度的均匀增大,三维弹塑性弯曲裂纹尖端塑性区的最大值和变化幅值不断减小,减小的幅度越来越小,最终趋于平面应变状态下的弹塑性弯曲裂纹尖端塑性区尺寸最大值和变化幅值.当三维裂纹体几何尺寸相同时,三维弯曲裂纹尖端塑性区的最大值和变化幅值随外载荷的不断增大而逐渐增大.建立了一个计算三维弹塑性弯曲裂纹交变塑性区的最大值和变化幅值的崭新理论模型.     

准静载作用下弹塑性微弯裂纹张开位移

综合考虑了准静态作用应力,塑性区域边界上正应力与剪应力,利用二阶摄动方法与卡氏定理计算了弯曲裂纹尖端的张开位移。研究了在不同的准静载荷条件下弹塑性弯曲延伸裂纹尖端张开位移随着弯曲裂纹形状参数的变化而变化的规律。研究表明,当初始裂纹长度与弯曲路径的形状参数为定值时,弯曲延伸裂纹尖端张开位移大小随外载荷的增大而增大,且增加的趋势非常剧烈。     

用裂纹张开位移计算三点弯曲试样的动态应力强度因子

给出了一种由裂纹的动态张开位移计算三点弯曲试样的动态应力强度因子的简单方法。对于两种不同几何尺寸的试样,在三类不同载荷作用下给出了数植算例,并与完全的动态有限元方法的计算结果进行了比较。结果表明:两种方法的计算结果相当一致。最后,还给出了由测定三点弯曲试样的裂纹张开位移确定试样的动态应力强度因子,最终确定材料动态起裂韧性的方法。     

I型裂纹尖端约束应力区模型及其解析解

考虑了I型裂纹尖端损伤区域内三种不同的约束应力分布形式,即右三角分布形式(情况A)、均匀分布形式(情况B)、左三角分布形式(情况C),并采用复变函数方法求得了应力强度因子与裂纹张开位移的解析解;在此基础上,通过数值计算得到了应力强度因子和裂纹张开位移随约束应力区长度、约束应力大小以及分布形式的变化规律。研究结果表明:随裂尖材料损伤程度的增加,裂尖损伤区内约束应力减小,应力强度因子和裂纹张开位移增大;约束应力的分布形式对应力强度因子和裂纹张开位移有显著影响;相对于其他区域,约束应力对裂纹尖端区域裂纹张开位移的影响较大。然而,对于裂尖损伤区域的形成与作用荷载、材料性质、构件几何尺寸之间的关系,还需要进行更为深入的研究。     

冲击载荷下两裂纹间的连通规律

脆性材料内部含有大量裂纹，当某一裂纹扩展时，其他裂纹会对扩展裂纹产生影响。为了研究冲击载荷下，脆性材料内两裂纹的相互影响、连通规律及裂纹尖端应力强度因子的变化规律，利用有机玻璃板制作了含非平行双裂纹的实验试件，利用落板冲击设备进行了中低速冲击实验，结合有限元分析软件ABAQUS计算出裂纹尖端应力强度因子，利用有限差分软件AUTODYN进行了动态数值模拟研究，并将其模拟结果与实验结果进行对比分析。实验及模拟结果表明:裂纹破坏形态与AUTODYN数值模拟破坏形态基本一致；试件的断裂形态随着两裂纹间距不同而不同；裂纹间的相互影响程度随着裂纹间间距增大而减小；裂纹尖端应力强度因子K_I随着裂纹间距的增大而减小，而K_II随着裂纹间距增大而增大。     

三点弯曲试样动态冲击特性的有限元分析

本文使用动态有限元技术，对于两种不同几何尺寸，两种不同材料的三点弯曲试样在三类七种不同冲击载荷作用下的动态响应进行了分析，求得了动态应力强度因子随时间的变化规律。并与准静态应力强度因子进行了比较。计算结果表明：将冲击载荷历史代入静态公式确定动态应力强度因子的做法是不正确的，要求得动态应力强度因子，必须对试样进行完全的动态分析。当材料的Ｅ／ρ值相同时，动态应力强度因子的响应曲线完全相同。而动态应力强度因子分别与加载点的位移及裂纹的张开位移之间存在着与准静态情况下各自相同的线性关系。这与资料［５］［６］中的结论完全相同。     

弹塑性疲劳微弯裂纹尖端塑性区问题

主要研究疲劳载荷作用下弹塑性裂纹弯曲延伸扩展问题.通过分析论证,比较精确地研究了疲劳载荷作用下弯曲延伸裂纹尖端塑性区域边界上交变应力的分布状况.综合考虑了疲劳作用应力,塑性区域交变应力,利用二阶摄动方法,研究计算了弯曲延伸裂纹尖端塑性区域的范围,并预测了疲劳载荷作用下弹塑性裂纹扩展路径.     

冷喷涂试件疲劳裂纹扩展规律试验研究

冷喷涂作为一种新兴的表面处理技术,广泛应用于增材制造和零部件修复等领域。为了探究冷喷涂处理后Q355钢基体的疲劳裂纹扩展规律,对2组标准单边缺口3点弯曲试样进行了冷喷涂处理。在光滑的Q355B钢基材表面分别沉积了纯Al和A5052铝合金涂层,然后对冷喷涂试件和一组未喷涂光滑试件进行了3点弯曲疲劳试验,得到了裂纹尖端张开位移和裂纹长度、裂纹扩展速率和荷载循环次数的规律曲线并进行了对比分析。结果表明：在裂纹扩展长度相同的情况下,冷喷涂试件和未喷涂试件的裂纹尖端张开位移基本相同,且随着疲劳裂纹的延伸,裂纹尖端张开位移也随之快速增大;在一定的裂纹尖端张开位移范围内,冷喷涂处理可以降低疲劳裂纹扩展速率;采用裂纹尖端张开位移作为疲劳裂纹扩展控制参数对冷喷涂试件的疲劳裂纹扩展规律进行判定是准确的,且裂纹尖端张开位移通过试验容易获得,简单方便,可以同时满足裂纹尖端弹性和塑性的情况。     

圆柱形界面相裂纹在扭转载荷作用下的动态断裂

本文研究了位于界面相中的圆柱形界面裂纹的扭转冲击问题.采用Laplace、Fourier变换和位错密度函数将混合边值问题转化为求解Cauchy核奇异积分方程,利用Laplace数值反演技术计算了动态应力强度因子.讨论了材料特性和结构的几何尺寸对动态应力强度因子的影响.结果表明,随着界面相厚度的增加,无量纲化的动态应力强度因子减小.当裂纹靠近剪切弹性模量大的材料时,无量纲化的动态应力强度因子增大,反之减小.界面相两侧不同的材料组合对裂尖动态应力强度因子的影响是随着剪切弹性模量和质量密度的比值的增加而减小.界面相中裂纹长度对裂尖动态应力强度因子的影响比其他因素的影响大.     

不同韧性金属扩展裂纹尖端Gao—Hwang奇异场的实验研究

用云纹法和光学空间滤波技术,测量了六种不同应变硬化指数(n)的铝和铜金属材料双边裂纹,单向拉伸试件的扩展裂纹尖端三维位移场.利用试验得到的位移场,分析了位移奇异性,并与G-H 理论解进行了比较.由试验的位移场数据确定了理论解中两个待定常数A 和ε_■,给出了Ⅰ型、平面应力、幂硬化材料,扩展裂纹尖端奇异场的比较形式.在理论与试验位移场相差±10%的误差范围内,确定了试验的G-H 奇异场主导区范围、形状,并对结果进行了分析.试验表明:扩展裂纹尖端存在[ln(A/r)]~■奇异主导区.在本试验应变硬化指数为n=3.5→14的六种材料范围内,这个主导区形状由蝶形发展到扁圆或圆形.G-H 奇异主导区的尺寸和形状与材料、试件几何尺寸、外载形式有关.在G-H 场内部存在着三维变形区,裂纹尖端断裂过程区在此三维变形区内.随着外载荷不断增加,裂尖三维变形区内将出现典型的韧性损伤现象:首先在晶界或二相夹杂处,出现孔洞,然后孔洞逐渐长大,汇合,导致宏观裂纹扩展.载荷比较低时,在G-H 场外边还将有弹性场存在,随着载荷增加,G-H 场也在向外扩大.     

Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture

Analyses of the stress and strain fields around smoothly-blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane-strain yielding and subject to mode I opening loads, have been carried out by use of a finite element method suitably formulated to admit large geometry changes. The results include the crack-tip shape and near-tip deformation field, and the crack-tip opening displacement has been related to a parameter of the applied load, the J-integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power-law hardening materials. The J-integral is found to be path-independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void-growth near the tip in hardening materials seems to be little different from the rate in non-hardening ones when measured in terms of crack-tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these effects are discussed. The implications of the finite element results for fracture criteria based on critical stress or strain, or both, is discussed with respect to transition of fracture mode and the angle of initial crack-growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.     

含力磁屈服区的压磁材料硬币型裂纹问题研究

本文利用Hankel 变换及Copson 求解方法,得到了在无穷远处磁荷载以及对称力荷载作用下的无限大压磁材料中,硬币型裂纹在裂纹尖端含有环状力磁双屈服区情况下的相关解析解．本文考虑了磁屈服区尺寸小于、大于、等于力屈服区尺寸的三种情况．结果表明：屈服区尺寸不仅与外荷载及材料常数相关,更与力磁屈服区尺寸的相对大小有关;其中,较大尺寸的屈服区仅受同性质单一荷载影响,与材料常数无关;而较小尺寸屈服区受力磁两荷载与材料常数共同影响;裂纹张开位移、磁势跳变均沿裂纹面径向增大而减小;裂尖张开位移、裂尖磁势跳变与材料常数相关,且随外荷载增大而增大．     

THE EXACT SOLUTIONS OF ELASTIC－PLASTIC CRACK LINE FIELD FOR MODE ⅡPLANE STRESS CRACK

ＴＨＥＥＸＡＣＴＳＯＬＵＴＩＯＮＳＯＦＥＬＡＳＴＩＣ－ＰＬＡＳＴＩＣＣＲＡＣＫＬＩＮＥＦＩＥＬＤＦＯＲＭＯＤＥＩＩＰＬＡＮＥＳＴＲＥＳＳＣＲＡＣＫＹｉＺｈｉｊｉａｎ（易志坚）ＷａｎｇＳｈｉｊｉｅ（王士杰）ＷａｎｇＸｉａｎｇｊｉａｎ（王向坚）（Ｒｅｃｅ...     

Analysis of dynamic growth of a tensile crack in an elastic-plastic material

The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J₂ flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.     

Elastoplasticity of crack loaded by two pairs of isolated shear forces in finite width plate

The failure behavior of an elastic-perfectly plastic body with a crack loaded by two pairs of concentrated shear forces is discussed. The analytical solutions of an eccentric crack in a finite plate loaded by two pairs of point shear forces are obtained. It includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near crack line and the law of the plastic zone along the crack line with external loads. The solutions of this paper are sufficiently precise near the crack line in elastic-perfectly plastic materials. Subsequently, the present results are compared with solutions based on the minimum strain energy density theory and elastic-plastic solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

弯载下位于刚性固定端周向壁穿裂纹的圆柱壳弹塑性解

金属圆柱壳结构常见于大型复杂结构系统中。这类构件在其端部与其它构件相连接是工程上常见的结构形式。由于连接处焊接热影响或实际复杂内力的作用,在连接处产生疲劳裂纹的几率相对增大;另一方面,由于高韧性材料的应用,使得弹塑性裂纹更为常见。然而到目前为止尚无这类问题的弹塑性理论解析。本文针对受弯曲载荷作用下的周向壁穿裂纹位于固定端的圆柱壳,基于半膜力壳理论及Dugdale模型,推导了裂纹尖端张开位移(CTOD)和裂纹尖端张开角度(CTOA)等一套相对完整的弹塑性解析解。该解除少数数值求根外,均为显式表达,可用于裂纹起裂、撕裂计算,追踪此类由弹塑性裂纹的存在所引起的圆柱壳结构的柔度以及裂纹撕裂条件下的极限承载能力等变化过程,弥补了这类工程问题解析解空缺的不足。     

Analysis to the stress and strain structures of mode I 3-D crack in elastic-plastic state

In this paper, the stress and strain structures of Mode I 3-D crack in power hardening material are studied by analyzing the fundamental equations of elastic-plastic mechanics. It is shown that three regions, Z1,Z2 and Z3 can be divided in the thickness direction according to the stress characteristic. In region Z1, the stress components in the plane Perpendicular to z axis (thickness direction) can be solved first using the fundamental equations of plane strain state; in region Z3, they can be solved first by the equations of plane stress state. The region Z2 is defined as a transition layer. It is shown that the transition layer is the characteristic of Mode I 3-D crack in elastic-plastic state, and it is significant to the research on 3-D fracture. The crack tip opening displacement CTOD is chosen to describe the amplitude coefficient of the local stress field, and the distribution of CTOD in 3-D state is investigated.The project supported by National Natural Science Foundation of China.     

Elastoplastic solution for an eccentric crack loaded by two pairs of point tensile forces

The strain energy density theory and the near crack line analysis method are applied to investigate an eccentric crack loaded by two pairs of tensile point forces in a finite plate. The minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. Obtained is the elastic-plastic solution near the crack line of an eccentric crack loaded by two pairs of point tensile forces under large scale yielding condition. More specifically, the near field solution contains the unit normal vector of the elastic-plastic boundary and the elastic-plastic stress field. The length of the plastic zone along the crack line is found to vary with the external load and the bearing capacity of a finite plate with an eccentric crack loaded by two pairs of tensile point forces. Compared with small scale yielding condition, the normalized load obtained is higher than those under small scale yielding condition when the length of the plastic zone is the same.