断层岩爆是应变局部化导致的系统失稳回跳

讨论了应变局部化、岩爆及Ⅱ类变形行为的关系，并利用梯度塑性理论得到了4种等效的回跳准则。局部化是岩爆的前兆之一，也是出现Ⅱ类变形行为的原因。利用最小势能原理及梯度塑性理论，可得到系统的失稳判据；利用位移法，可以得到系统的Ⅱ类变形行为。若非弹性剪切位移(或平均塑性剪切应变)的增加快于弹性剪切位移(或平均弹性剪切应变)的降低，将出现Ⅰ类变形行为；反之，将出现Ⅱ类变形行为。弹性区与剪切带宽度的比率越大，或剪切弹性模量与剪切降模量的比率越小，系统越容易失稳。     

准脆性材料试件应变软化尺度效应理论研究

研究了由于剪切局部化而引起的试件长度的尺寸效应，基于可以考虑微结构相互作用的非局部理论，得到了非局部塑性剪应变与局部塑性剪应变及其二阶应变梯度的关系，通过获得剪切带内部的塑性剪切应变，得到了岩样轴向的平均应变与位移的理论关系，研究结果表明，这一关系具有尺寸效应，随着试件高度的增加，应力-应变曲线变陡，当试件高度非常大时，发生Ⅱ类变形行为，而且，随着剪切带倾角的增加，应力-应变曲线也变陡，将理论结果与前人的试验结果进行了比较，结果表明吻合良好。     

ANALYSIS ON INCLINATION ANGLE OF SHEARBAND UNDER LOW CONFINING PRESSUREBASED ON GRADIENT-DEPENDENT PLASTICITY

The inclination angle ofsbear band is analyzed considering heterogeneity of rock material when a single shear hand is formed in the center of specimen under triaxial compression. The analytical solution of post-peak axial stress-axial strain curve is deduced using the assumption that the total post-peak deformation is composed of entire uniform elastic deformation and localized shear plastic deformation dependent on the thickness of shear band. The obtained solution shows that the post-peak stiffness is related to the inclination angle of shear band, confining pressure, thickness of shear hand and elastic modulus, etc. Using the solution, the expression for the inclination angle of shear hand can be presented easily and it is dependent on constitutive parameters of rock material and geometry parameters of rock specimen. Larger dilation angle or loading rate leads to increment of the inclination angle. In addition, the inclination angle increases with the thickness of the shear band, which cannot be explained or forecasted by other existing solutions, such as Coulomb inclination, Roscoe inclination and Arthur inclination, etc.     

单轴压缩湿土样最大剪切应变场数字图像相关方法结果的统计分析

研究了单轴压缩湿土样沿剪切带方向的最大剪切应变的均值和标准差以及剪切局部化区域尺寸的演变规律。为了深入揭示土样剪切带萌生的过程,根据纵向应变较高时清晰剪切带所处位置在土样上布置测线,对由数字图像相关方法获得的结果进行双三次样条插值,从而获得测线上光滑性较好的最大剪切应变分布。研究发现,随着纵向应变的增加,沿剪切带方向的最大剪切应变由低值多峰向高值少峰转变。测线上最大剪切应变发生突增的点、局部高值点及低值点均有可能发展成为主峰。测线上最大剪切应变的均值和标准差随纵向应变的演变规律在总体上均呈上凹形,但当纵向应变较低时,二者均呈线性。以上述两种统计量线性规律丧失所对应的平均最大剪切应变作为剪切带萌生的条件。随着纵向应变的增加,土样中发生剪切局部化的区域越来越大。欲达到相同的剪切局部化区域尺寸,含水率高的土样所要求的纵向应变较高。当纵向应变较高时,含水率高的土样的剪切局部化区域尺寸比含水率低的土样要大,这与其塑性变形阶段较长有关。     

关于潘岳讨论的答复

首先十分感谢潘岳教授及申建红讲师对拙作“准脆性材料应变软化尺度效应理论研究”(以下简称“原文”,作者:王学滨,潘一山,杨小彬)的关注和有益讨论。现就潘岳教授等所提出的问题,尽己所能答复如下。 1 梯度塑性理论的实质是考虑材料的非均质性 潘岳教授等在讨论的第一段中指出:“岩石的破坏不同于金属,但仍可以采用变形局部化及变形梯度效应的概念来对其软化阶段特性进行某些研究”。我们对此也十分赞同。 梯度塑性理论是经典弹-塑性理论的推广和完善方法之一。常规作法是将非局部塑性剪切应变替代经典弹-塑性理论中的塑性剪切应变,这样…     

Ti-6Al-4V绝热剪切带的厚度及应变率效应研究

通过引入与Batra及Kim类似的论点,将绝热剪切带宽度定义为绝热剪切带的中心区域的宽度(w5%),在该区域上温度比其峰值小5%,利用Johnson-Cook模型及梯度塑性理论分析Ti-6Al-4V绝热剪切带的厚度及应变率的影响.计算表明,在名义应变率的下限(800s-1)及上限(1400s-1)之间,当绝热剪切带的总厚度选取为0.3235及0.0705 mm时,计算结果非常接近于绝热剪切带宽度的上限(55 um)及下限(12 um).当应变率较低时,绝热剪切带较宽.随着应变率的增加,绝热剪切带宽度快速降低.在高应变率时,绝热剪切带宽度基本保持恒定.该理论结果与Dodd及Bai的理论结果有类似之处,与Weerasooriya及Beaulieu针对钨合金的实验结果非常一致,与Klepaczko及Rczaig的数值结果的前半部分相似.     

单向压缩条件下圆形颗粒体含孔洞试样的力学模拟

通过编程,用连续介质快速拉格朗日分析(FLAC)实现了圆形颗粒体在单向压缩条件下的力学行为模拟.颗粒体试样中间含一圆形孔洞,颗粒体被离散成正方形网格,若2个颗粒体发生接触,则需要在颗粒体之间预置界面.研究了施加的荷载对试样应力线、应变线及受拉破坏区域等的影响.结果表明,试样内部的最大压应力约为所施加压应力值的5倍,这有别于连续介质理论的结果.孔洞顶部及底部各有1个三角形受拉区,内部可见明显的拉裂纹,裂纹的长度随试样端部所施加应力的增加而增大.     

剪切带内部应变(率)分析及基于能量准则的失稳判据

应用应变梯度塑性理论对局部化剪切带内部(塑性)剪应变(率)规律进行了理论分析。研究了剪切降模量及岩石材料内部长度等参数对剪切带内部应变(率)的影响。推导了剪应力(率)与剪切带相对错距(速度)的本构关系。研究了剪切降模量和岩石材料内部长度对剪切带稳定性的影响。将岩石试件直剪试验试验机简化为钢块,采用能量准则对岩石试件(剪切带)及钢块系统的稳定性进行了理论研究,提出了系统失稳判据。研究表明:岩石材料的剪切降模量越大,岩石材料的内部长度越小,试验机的剪切刚度越小及试验机的等效高度越大剪切带--钢块系统越容易失稳。     

Analysis of damage localization for ductile metal in process of shear band propagation

1 Introduction Shear localization is an important and often dominating deformation and failure mechanism for Ti and Ti alloy in dynamic loadings[1—10]. The eventual outcome of localized deformation is ductile rupture and material separation. Shear locali…     

Localized shear deformation during shear band propagation in titanium considering interactions among microstructures

Closed-form analytical solutions of plastic shear strain and relative plastic shear displacement during shear band propagation are proposed under dynamic loadings based on gradient-dependent plasticity considering the effect of microstructures due to heterogeneous texture of Ti. According to the differences in shear stress levels, Ti specimen is divided into three regions: residual region, strain-softening region and elastic region. Well-developed shear band is formed in the residual region and the relative plastic shear displacement no longer increases. In the normal and tangential directions, the plastic strain and the displacement are nonuniform in the strain-softening region.At the tip of shear band, the shear stress acting on the band is increased to shear strength from the elastic state and the shear localization just occurs. Prior to the tip, Ti remains elastic. At higher strain rates, the extent of plastic strain concentration is greater than that under static loading. Higher strain rate increases the relative plastic shear displacement. The present analytical solution for evolution or propagation of shear localization under nonuniform shear stress can better reproduce the observed localized characteristics for many kinds of ductile metals.