Ⅱ型动态扩展裂纹尖端的弹黏塑性渐近场

考虑材料的黏性效应建立了Ⅱ型动态扩展裂纹尖端的力学模型,假设黏性系数与塑性等效应变率的幂次成反比,通过分析使尖端场的弹、黏、塑性得到合理匹配,并给出边界条件作为扩展裂纹定解的补充条件,对理想塑性材料中平面应变扩展裂纹尖端场进行了弹黏塑性渐近分析,得到了不含间断的连续解,并讨论了Ⅱ型裂纹数值解的性质随各参数的变化规律.分析表明应力和应变均具有幂奇异性,对于Ⅱ型裂纹,裂尖场不含弹性卸载区.引入Airy应力函数,求得了Ⅱ型准静态裂纹尖端场的控制方程,并进行了数值分析,给出了裂纹尖端的应力应变场.当裂纹扩展速度(M→0)趋于零时,动态解趋于准静态解,表明准静态解是动态解的特殊形式.     

某抽水蓄能电站地下洞室围岩岩体质量特征分析

考虑材料的黏性效应建立了II型动态扩展裂纹尖端的力学模型,假设黏性 系数与塑性等效应变率的幂次成反比,通过分析使尖端场的弹、黏、塑性得到合理匹配,并 给出边界条件作为扩展裂纹定解的补充条件,对理想塑性材料中平面应变扩展裂纹尖端场进 行了弹黏塑性渐近分析,得到了不含间断的连续解,并讨论了II型裂纹数值解的性质随各参 数的变化规律. 分析表明应力和应变均具有幂奇异性,对于II型裂纹,裂尖场不含弹性卸载 区. 引入Airy应力函数,求得了II型准静态裂纹尖端场的控制方程,并进行了数值分析, 给出了裂纹尖端的应力应变场. 当裂纹扩展速度($M\to 0$)趋于零时,动态解趋 于准静态解,表明准静态解是动态解的特殊形式.     

I型定常扩展裂纹尖端的弹黏塑性场

考虑材料在扩展裂纹尖端的黏性效应，假设黏性系数与塑性应变率的幂次成反比，对幂硬化材料中平面应变扩展裂纹尖端场进行了弹黏塑性渐近分析，得到了不含间断的连续解，并讨论了I型裂纹数值解的性质随各参数的变化规律. 分析表明应力和应变均具有幂奇异性，并且只有在线性硬化时，尖端场的弹、黏、塑性才可以合理匹配. 对于I型裂纹，裂尖场不含弹性卸载区. 当裂纹扩展速度趋于零时，动态解趋于准静态解，表明准静态解是动态解的特殊形式；如果进一步考虑硬化系数为零的极限情况，便可退化为Hui和Riedel的非线性黏弹性解.     

裂纹面摩擦接触引起的断裂韧性增长的研究

采用弹黏塑性的材料本构关系, 建立了压、剪混合型裂纹常速准静 态扩展的力学模型, 求得了裂纹面摩擦接触条件下裂纹尖端场的数值解, 并基于数 值结果讨论了扩展裂纹的摩擦效应. 计算和分析表明, 裂纹面的摩擦效应主要表现 在两个方面. 第一方面是摩擦会导致裂纹尖端区材料的断裂韧性增高, 并且裂纹面间的摩擦作用越强, 增韧效果越显著. 摩擦增韧的机制可以解释为裂纹 面间的摩擦作用导致裂纹尖端塑性区尺寸变大, 使裂纹尖端场的塑性变形能增加, 从而使得裂纹尖端区材料增韧. 摩擦生热并不是导致材料断裂韧性增长的根本机制. 第二方面是摩擦会导致``断裂延缓'. 利用裂纹面的摩擦来提高构件的承载能力和延长构件的服役寿命具有较大的工程实用价值.     

双材料界面Ⅰ型扩展裂纹尖端的弹黏塑性场

双材料界面中存在材料黏性效应, 对界面裂纹尖端场的分布和界面本身性能 的变化起着重要的影响. 考虑裂纹尖端的奇异性, 建立了双材料界面扩展裂纹尖端的弹黏塑 性控制方程. 引入界面裂纹尖端的位移势函数和边界条件, 对刚性-弹黏塑性界面I型界面 裂纹进行了数值分析, 求得了界面裂纹尖端应力应变场, 并讨论了界面裂纹尖端场随各影响 参数的变化规律. 计算结果表明, 黏性效应是研究界面扩展裂纹尖端场时的一个主要因素, 界面裂纹尖端为弹黏塑性场, 其场受材料的黏性系数、马赫数和奇异性指数控制.     

蠕变材料Ⅰ型动态扩展裂纹尖端场

为了研究黏性效应作用下的动态扩展裂纹尖端渐近场，建立了蠕变材料Ⅰ型动态扩展裂纹的 力学模型.首先，依据在稳态蠕变阶段，弹性变形和黏性变形同时在裂纹尖端场中占主导地 位，由量级协调可知，应力和应变具有相同的奇异量级，即(σ,ε)∝/ r- 1/(n-1). 其次，通过渐近分析推导出动态扩展裂纹尖端场的控制方程并求得了裂纹尖端应 力、应变和位移分离变量形式的渐近解.最后，采用双参数打靶法求得了裂纹尖端应力、应 变的数值结果.数值计算表明，裂尖场主要受材料的蠕变指数n和马赫数M的控制；在Ⅰ 型动态扩展裂纹前方，环向应变达到最大值，可据此建立断裂准则. 由于裂纹稳定扩展与非稳定扩展的主奇异项相同，因此对于稳定扩展裂纹的渐近分析方 法，同样适用于非稳定的裂纹扩展问题.     

压剪载荷作用下界面裂纹尖端场的研究

建立了弹性-幂律蠕变双材料界面裂纹准静态扩展的力学模型，求得了裂纹尖端应力、应变和位移场分离变量形式的解及其数值结果；讨论了材料性能参数对裂纹尖端场的影响；计算和分析了界面裂纹的摩擦效应，并且得出了给定条件下裂尖场的轮廓图形．     

可压缩粘弹性材料Ⅱ型动态扩展裂纹尖端场

为了研究粘性效应作用下的动态扩展裂纹尖端渐近场,建立了可压缩粘弹性材料II型动态扩展裂纹的力学模型,推导了可压缩材料Ⅱ型动态扩展裂纹的本构方程.在稳态蠕变阶段,弹性变形和粘性变形同时在裂纹尖端场中占主导地位,应力和应变具有相同的奇异量级r-1/(n-1).通过渐近分析求得了裂纹尖端应力、应变和位移分离变量形式的渐近解,并采用打靶法求得了裂纹尖端应力、应变和位移的数值结果,给出了应力、应变和位移随各种参数的变化曲线.数值计算表明,弹性变形部分的可压缩性对Ⅱ型裂尖应力场影响甚微,而对应变场和位移场影响较大.裂尖场主要受材料的蠕变指数n和马赫数M的控制.当泊松比ν =0.5时,可以退化为不可压缩粘弹性材料Ⅱ型动态扩展裂纹.     

蠕变硬化材料中Ⅱ型扩展裂纹尖端场特性研究

采用弹牯塑性力学模型,对蠕变硬化材料中平面应变扩展裂纹尖端场进行了渐近分析.假设人工粘性系数与等效塑性应变率的幂次成反比,通过量级匹配表明应力和应变均具有幂奇异性,奇异性指数由粘性系数中等效塑性应变率的幂指数唯一确定.通过数值计算讨论了Ⅱ型准静态扩展裂纹尖端场的分区构造以及裂纹尖端应力和应变场的特性随各材料参数的变化规律,结果表明裂尖场由材料的粘性和塑性共同主导.当硬化系数为零时裂尖场可退化为相应的HR场.     

动态裂纹尖端弹粘塑性场的研究

本文利用弹一粘一塑性材料力学模型，对动态扩展裂纹尖端的指数奇异性和对数奇异性进行了渐近分析。文中假定，弹性阶段的粘性效应可以略去，仅在塑性应变中粘性才起作用，对于这种模型，推导出了其率敏感型的本构关系。以Ⅱ型裂纹为例，进一步推导了两种奇异性下裂纹尖端场的渐近微分控制方程，并进行了数值仿真分析。同时讨论了粘性系数α、马赫数M^2对裂纹尖端应力应变场的影响，即，弹粘塑性材料扩展裂纹的奇异性取决于其粘性系数和马赫数，粘性系数较大时，裂纹尖端场具有对数奇异性；粘性系数较小时，裂纹尖端场具有指数奇异性。修正了文献中对数奇异性区域的大小；解释了文献中过渡区的成因；给出了过渡区尖端应力场解的形式，从而建立了裂纹尖端场的统一解。     

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.     

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.     

Field structure at mode Ⅲ dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

Field structure at mode III dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

粘弹塑性材料动态裂纹尖端场

本文采用一种弹性/粘塑性模型,对扩展裂纹尖端应力应变场进行了渐近分析。文中假定,弹性阶段的粘性效应可以略去,仅在塑性应变中粘性才起作用。对这种模型,文中导出了一种率敏感型的本构关系。并进一步导出了裂纹尖端应力应变场的动力学方程。通过量级分析,给出了尖端场的应力应变奇异性指数。并且讨论了弹性,塑性及粘性三者的匹配条件。对Ⅲ型裂纹进行了具体的分析计算。对各个不同参数的选取进行了详细的分析,讨论了解的性质随各参数的变化规律。     

Elastic-viscoplastic fields near the tip of a propagating crack under anti-plane shear

The elastic-viscoplastic model proposed by Bingham was used to analyse the stress and strain surrounding the tip of a propagating crack under antiplane shear. The proper displacement pattern was given ; the asymptotic equations were derived and solved numerically. The analysis and calculation show that for smaller viscosity the crack-tip possesses logarthmic singularity, and for larger viscosity it possesses power-law singularity.In critical case, the two kinds of singularity are consistent with each other. The result revealed the important role of viscosity for crack-tip field.     

VISCOPLASTIC SOLUTION TO FIELD AT STEADILY PROPAGATING CRACK TIP IN LINEAR- HARDENING MATERIALS

An elastic-viscoplastic constitutive model was adopted to analyze asymptotically the tip-field of moving crack in linear-hardening materials under plane strain condition. Under the assumption that the artificial viscosity coefficient was in inverse proportion to power law of the rate of effective plastic strain, it is obtained that stress and strain both possess power law singularity and the singularity exponent is uniquely determined by the power law exponent of the rate of effective plastic strain. Variations of zoning structure according to each material parameter were discussed by means of numerical computation for the tip-field of mode Ⅱ dynamic propagating crack, which show that the structure of crack tip field is dominated by hardening coefficient rather than viscosity coefficient. The secondary plastic zone can be ignored for weak hardening materials while the secondary plastic zone and the secondary elastic zone both have important influence on crack tip field for strong hardening materials. The dynamic solution approaches to the corresponding quasi-static solution when the crack moving speed goes to zero, and further approaches to the HR (Hui-Riedel) solution when the hardening coefficient is equal to zero.     

稳恒扩展裂纹尖端的弹粘塑性场

采用弹粘塑性力学模型代替通常的弹塑性模型，对于I型和Ⅱ型问题，分别求得了不可压缩材料中平面应变动态扩展裂纹尖端的指数奇异性场和对数奇异性场，消除了弹塑性解中存在的塑性激波。通过数值计算，分别求得了两种奇异属性的分界线，建立起统一的裂纹尖端奇异性场。