求解I型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量. 目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务. 以J积分为参量的材料断裂测试中应用最广的是I型裂纹试样的断裂韧性测试. 本文在平面应变条件下,针对断裂韧性测试中使用的6种I型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数. 分析表明,6种I型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好. 新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值. 应用新方法可便于获得各类I型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.      

J-integral evaluation of nanoclay-modified HDPE/PA6 microfibrillar composites

Microfibrillar composites (MFC) are polymer-polymer composites with many advantages, including good dispersion and bonding of in-situ generated fibrils. Recently, it has been shown that their performance can be enhanced by suitable addition of organophilized montmorillonite (oMMT) provided the numerous oMMT-induced effects are harmonized. This work deals with evaluation of resistance against unstable crack propagation (J-integral) in combination with Charpy and tensile impact strength methods, and SEM observation of fibrils shape and size and fracture surfaces. The results indicate that addition of PA6 inclusions and oMMT to relatively ductile HDPE reduces toughness evaluated using Charpy and J-integral. The fact that tensile impact strength is not reduced by oMMT indicates the importance of the impact testing mode for MFC. Of importance is the fact that formation of PA6 fibres reinforced with oMMT practically does not reduce toughness. Hence, the drawn oMMT-modified system with significantly higher stiffness and practically unchanged fracture resistance can be obtained. Combination of the complex effect of oMMT and in-situ fibrils reinforcement present a tool to attain polymer systems with enhanced well-balanced properties.     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.     

动态J积分及Rice J积分一致性比较与分析

首先回顾了动态J积分的发展进程,然后给出了两种常用动态J积分和Rice J积分的数学计算式,并对它们的一致性加以讨论,由此提出一种广义J积分的定义。然后通过算例,基于ANSYS软件,建立平面应变情形下纯I型中心裂纹模型,并利用编写的APDL程序计算了各个J积分,通过结果比较,进一步验证了在动态加载条件下,动态J积分比Rice J积分具有更好的路径守恒性,但仍可以看出它们的取值具有一定的一致性。最后,通过J积分间接法和裂尖位移外推法分别计算裂纹动态应力强度因子,所得结果吻合很好,验证了编写程序的正确性。     

An extension of the J-integral to piezoelectric materials

This paper provides an analysis of the crack propagation criterion for a thin piezoelectric plate with a symmetry of order six. On the basis of Gol’denveizer’s asymptotic integration method or Destuynder’s unidirectional zoom technique, we obtain an extension of the purely mechanical J-integral to piezoelectric materials, with a dependence of the gradient of energy of the plate only on zeroth order terms of asymptotic expansions.     

On the determination of the point of fracture initiation by the load separation criterion in J-testing of ductile polymers

The application of an experimental approach based on the load separation criterion for the determination of the point of fracture initiation in a fracture test on a ductile polymer was critically examined. To this aim, the fracture process outlined by the application of this method was related to that described by the visual analysis of the fracture surfaces obtained in fracture tests on nominally identical specimens, in which different levels of crack extension were produced. The material examined was an acrylonitrile-butadiene-styrene (ABS) resin, and the fracture tests were performed at low loading rate on single-edge notched in bending specimens.The results demonstrated that this load separation criterion based methodology is a promising approach for the determination of the point of fracture initiation, and for material fracture resistance, J_Ic, evaluation. The method also has experimental simplicity and a high degree of repeatability.     

含中心裂纹梯度纳晶金属的数值模拟

梯度纳晶金属由于其微观组织的梯度分布,力学属性也呈现梯度变化,这使得其表现出不同于传统均匀材料的断裂行为．利用材料力学参数的梯度分布来表征梯度纳晶金属中晶粒尺寸的梯度变化,并编写ABAQUS和MATLAB脚本程序建立分层有限元模型．通过数值模拟计算了含有初始中心裂纹的梯度纳晶金属在受远端均匀拉应力作用下的裂尖J积分,分别研究了屈服应力梯度、裂纹角度和裂纹长度对金属材料断裂韧性的影响,并与传统粗晶进行了对比．结果表明梯度纳米结构的存在导致梯度纳晶金属内部的中心裂纹两端表现出不同的断裂韧性,小晶粒一侧裂尖的抗裂韧性优于大晶粒一侧裂尖,且屈服应力梯度绝对值越大,两者差距越大．梯度纳晶金属的断裂韧性受中心裂纹角度和长度变化的影响与传统粗晶金属基本一致,同时在晶粒尺寸梯度的作用下梯度纳晶的裂尖J积分略低于粗晶,即整体上拥有更好的抗裂韧性．     

A finite element method based comparative fracture assessment of carbon black and silica filled elastomers: Reinforcing efficacy of carbonaceous fillers in flexible composites

This study is focused on numerical investigation on fracture behaviors of carbon black (CB) and silica filled elastomeric composites. Finite element analysis (FEA) in compliance with multi-specimen method is used to calculate J-integral and geometry factor of the rubber composites up to a displacement of 20 mm for single edge notch in tension (SENT) and double edge notch in tension (DENT) specimens. An empirical relationship between crack tip opening displacement (CTOD) and crack advancement is established depending on notch to width ratio (NWR). The stress contours across the notches for SENT and DENT specimens is discussed briefly. It is found that fracture propagation resistance of CB filled elastomer is 125% more than that of silica filled elastomer. Although, Silica filled elastomer have good tensile strength and crosslink density but it fails to replace carbon black in terms of fracture properties. The critical J-integral for CB filled elastomer is 18.7% and 32.2% more than silica filled elastomer for SENT and DENT specimens respectively. The effect of specimen type on various fracture properties is also explored. The factor of safety is found to be significantly more in case of CB filled elastomers making them less vulnerable to crack propagation and catastrophic failure.     

剪胶接结构的混合模式断裂分析

给出了Ｇｏｌａｎｄ－Ｒｅｉｓｓｅｎｅｒ型剪接结构的Ｊ积分表达在被粘物体小转角和胶层很薄的假设下与路径无关。Ｊ积分代表胶层厚度与胶层内最大能量密度的乘积。对单剪接接头，本文计算了裂纹在胶层内和界面上两种情况下的局部Ｉ型和Ⅱ型应力强度因子之比，即局部载荷相角，从而给出了单剪接接头的断裂判据。