基于临界距离点法的混凝土Ⅰ型断裂韧度的预测

混凝土的断裂韧度是极为重要的断裂力学材料参数，本文利用临界距离理论(TCD)中的点法和混凝土标准断裂梁试样裂缝尖端应力场的近似解，提出了一种对混凝土断裂问题按临界距离的点法进行分析的方法．基于已有文献的试验材料及其实验结果，分析了这种断裂研究分析方法的可行性．将临界距离点法与双K断裂准则应用于几何相似的混凝土梁的断裂韧性和断裂过程区分析，验证了TCD点法的可靠性．实验表明：临界距离理论的点法能够获得比双K断裂准则相对安全的失稳断裂韧度，利用临界距离法还可得到相应断裂过程区长度的极限估算值．     

U形切口的有限断裂准则

有限断裂力学准则综合了应力和能量参数,假设裂纹或切口端部有限裂纹长度的增长．特别地,该有限裂纹的长度不是材料的基本常数,而是与构件的结构有关．基于U形切口两种形式：点方式和线方式有限断裂准则,对文献中的铝合金U形切口三点弯曲断裂实验进行了分析验证．一方面基于材料的断裂韧度和抗拉强度,预测切口件断裂载荷;另一方面根据几组不同的切口根部半径及其对应的临界切口应力强度因子,同时估算材料的断裂参数：断裂韧度和抗拉强度．将点方式和线方式两种不同形式有限断裂准则的预测结果,与平均周向应力准则、最大周向应力准则以及文献中相关结果进行了比较得出：无论是预测断裂载荷还是估算材料断裂参数,线方式有限断裂准则,与文献中相关结果比较吻合,尤其是估算的断裂韧度精度较高．     

混凝土双K断裂参数计算的半解析有限元法

混凝土裂缝扩展的双$K$断裂准则，用于描述混凝土结构裂缝的起裂、稳定扩 展和失稳断裂. 其相应的双$K$断裂参数(起裂断裂韧度$K_{\rm IC}^{\rm ini} $和失 稳断裂韧度$K_{\rm IC}^{\rm un}$)一般通过简便的试验和基于虚拟裂缝扩展粘 聚力的解析方法确定. 利用平面扇形域哈 密顿体系的方程，通过分离变量法及共轭辛本征函数向量展开法，以解析的方法推导出基于混 凝土虚拟裂缝扩展线性粘聚力模型的平面裂缝解析元列式. 将该解析元与有限元相结合，构成 半解析的有限元法，可求解任意结构几何形状的混凝土平面裂缝双$K$断裂参数的计算问题. 数值计算结果表明半解析有限元法对该类问题的求解是十分有效的.     

双K断裂模型粘聚韧度KcIc实用插值计算方法

为了配合《水工混凝土断裂试验规程》在工程界的推广使用,提出了双K断裂模型中在临界状态时分布在虚拟裂缝上的粘聚力σ(x)产生的粘聚韧度KcIc的二元拉格朗日插值计算方法,进而由准脆性材料韧度三参数定律计算了混凝土起裂韧度KiInci。与粘聚韧度KcIc积分计算和简化计算方法的比较,表明此插值计算方法具有很高的精度,计算过程简化,使用计算器即可实现,便于工程人员实际使用。     

双K断裂模型粘聚韧度K_(Ic)~c实用插值计算方法

为了配合<水工混凝土断裂试验规程>在工程界的推广使用,提出了双K断裂模型中在临界状态时分布在虚拟裂缝上的粘聚力σ(x)产生的粘聚韧度K_(Ic)~c的二元拉格朗日插值计算方法,进而由准脆性材料韧度三参数定律计算了混凝土起裂韧度K_K~(ini).与粘聚韧度K_(Ic)~c积分计算和简化计算方法的比较,表明此插值计算方法具有很高的精度,计算过程简化,使用计算器即可实现,便于工程人员实际使用.     

一种弹塑性材料动态起裂韧度的J表征和测试方法

在数值计算的基础上提出了一个弹塑性材料动态起裂韧度的J表征和测试方法．这一方法利用自行研制的间接杆-杆型冲击拉伸试验装置，对周边切口的短圆柱试件实施基于一维试验原理的弹塑性材料动态断裂试验；利用试件两端的平均载荷—相对位移曲线(P-δ)或平均载荷-裂纹张开位移曲线(P-△)，推广Bice远场公式获得动态J积分；采用柔度变化率法确定裂纹起裂点，从而得到动态起裂韧度JJD．这一方法的优点在于利用P-δ或P-△曲线将外力对试件所做的与裂纹运动无关的质心惯性运动动能近似地从总能量中分离出来，且平均载荷P在起裂前以至失稳扩展前是单调增的，同时试验获得的P-δ和P-△曲线光滑，这使得用J积分作为裂纹尖端的表征参量以及用柔度变化率法确定起裂点和失稳点具有坚实的物理基础．     

基于数值模拟的混凝土系列有效断裂判据

基于ANSYS平台,对某系列混凝土断裂破坏试验的加载过程进行有限元数值模拟,获得了荷载-加力 点位移曲线.利用获得的曲线,在线性渐进叠加假定的基础上,确定了试件在失稳断裂时的临界有效裂缝长度.将模拟峰值荷载和临界有效裂缝长度代入由LEFM推导出的公式计算了考虑断裂过程区影响的有效断裂韧度.最后,通过对系列试验有效断裂韧...     

焊接热影响区断裂性能试验研究

钢框架梁柱节点在最近几次地震中经历了大量断裂破坏现象。可以采用杆端非线性弹簧模型对这种破坏模式进行数值模拟。为了确定断裂分析模型的参数，本文进行了结构钢（Q235c,Q345c)焊接热影响区断裂性能试验研究，获得了两种材料在焊接热影响区的JR阻力曲线。通过比较不同的断裂准则，考虑了裂纹失稳扩展前的稳态裂纹累计，根据J积分撕裂模量法建立了裂纹失稳的失效评定图。采用两种材料分别制作了一组外形尺寸一致，初始裂纹尺寸不同的单边裂纹焊接板，测出相应的极限拉伸应力，并和理论曲线进行了对比。最后，对于本文研究结果的适用范围做了说明。     

双相钢板料的单向拉伸断裂失效研究(Ⅱ)——弧长法非线性有限元分析

为了获得docol800DP双相钢板料的等效塑性应变和应力三轴度在单向拉伸断裂失效过程中的变化历程,对其拉伸过程进行了弧长法非线性有限元分析。根据试验得到的材料参数建立了双相钢单向拉伸试件的有限元模型,考虑大变形引起的几何非线性和塑性强化引起的材料非线性,模拟了试件拉伸变形的全过程。计算结果表明:弧长法可较好地模拟试件变形的全程,计算得到的典型变形阶段、集中性失稳带的分布及方向与试验结果吻合很好;发生失稳变形时的应变与理论分析结果一致。最后,给出了起裂点处失效参数的变化历程,为定量化研究双相钢材料的断裂失效模型提供准确的数据支持。     

轻质泡沫混凝土的劈裂破坏力学行为分析

利用平台巴西圆盘加载方式和钢质压条加载方式,对两种厚度为25mm和50mm、不同密度的轻质泡沫混凝土(400～1000kg/m3)进行巴西圆盘劈裂试验,研究密度和厚度对泡沫混凝土裂纹宽度、劈裂强度、断裂韧度、断裂能的影响规律。结果表明,在橡胶垫平台巴西圆盘和钢质压条加载方式下,其劈裂断裂特征大致分为四个阶段:线性弹性段、非线性弹性段、起裂阶段、失稳阶段。同样加载率下最大裂纹宽度随着泡沫混凝土密度增加逐渐减小,劈裂拉伸强度、断裂韧度、断裂能呈幂函数形式增加。借鉴Reinhardt非线性软化曲线,对不同密度泡沫混凝土的应力软化关系进行曲线拟合,建立基于拉伸强度、断裂韧度等控制参数的应力-裂纹宽度关系三段式模型。基于试验结果,对理想多孔材料细观力学预测模型进行修正,获得泡沫混凝土孔隙率与拉伸强度的半经验公式。     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

Modification of the fracture criterion for V-shaped notches (plane problem). Relationship between toughness and strength and structural parameters

A fracture criterion of the type of the Neuber-Novozhilov criterion is proposed to describe the fracture in the vicinity of the tip of a V-shaped notch under tensile and shear loading. In the proposed criterion, the limits of averaging of the stresses along the notch axis depend on the presence, location, and size of the initial defects in the material. The crystal lattice parameter of the initial material is chosen for the characteristic linear size. For a V-shaped notch subjected to tension and shear, simple equations are obtained that relate the stress intensity factors for the modified singularity coefficients, the singularity coefficients themselves, and the theoretical tensile and shear strengths of a single crystal of the material taking into account the damage to the material in the vicinity of the notch tip. The equations obtained allow a passage to the limit from a notch to a crack. It is shown that the classical critical stress intensity factor used in the strength analysis of cracked solids is not a material constant.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 106–115, January–February, 2005.     

Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading

Fracture phenomenon was investigated both experimentally and theoretically for a type of coarse-grained polycrystalline graphite weakened by a U-shaped notch under mixed mode loading. First, 36 disc-type graphite specimens containing a central U-notch, so called in literature as the U-notched Brazilian disc (UNBD), were prepared for four different notch tip radii and the fracture tests were performed under mode I and mixed mode I/II loading conditions. Then, the experimentally obtained fracture loads and the fracture initiation angles were predicted by using the U-notched maximum tangential stress (UMTS) and the newly formulated U-notched mean stress (UMS) fracture criteria. Both the criteria were developed in the form of the fracture curves and the curves of fracture initiation angle, in terms of the notch stress intensity factors (NSIFs). The results showed that while the criteria could predict successfully the experimental notch fracture toughness values, the UMS criterion provides slightly better predictions than the UMTS criterion, particularly for shear-dominant deformations. Also, found in this research was that the curves of fracture initiation angle were almost identical for the two criteria which both could predict well the experimental results.     

A MOVING CRACK IN A NONHOMOGENEOUS MATERIAL STRIP

This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum 'anti-plane shear' stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.     

Fracture toughness from the standpoint of softening hyperelasticity

Fracture toughness of brittle materials is calibrated in experiments where a sample with a preexisting crack/notch is loaded up to a critical point of the onset of static instability. Experiments with ceramics, for example, exhibit a pronounced dependence of the toughness on the sharpness of the crack/notch: the sharper is the crack the lower is the toughness. These experimental results are not entirely compatible with the original Griffith theory of brittle fracture where the crack sharpness is of minor importance.¹To explain the experimental observations qualitatively we simulate tension of a thin plate with a small crack of a finite and varying sharpness. In simulations, we introduce the average bond energy as a limiter for the stored energy of the Hookean solid. The energy limiter induces softening, indicating material failure. Thus, elasticity with softening allows capturing the critical point of the onset of static instability of the cracked plate, which corresponds to the onset of the failure propagation at the tip of the crack. In numerical simulations we find, in agreement with experiments, that the magnitude of the fracture toughness cannot be determined uniquely because it depends on the sharpness of the crack: the sharper is the crack, the lower is the toughness.Based on the obtained results, we argue that a stable magnitude of the toughness of brittle materials can only be reached when a characteristic size of the crack tip is comparable with a characteristic length of the material microstructure, e.g. grain size, atomic distance, etc. In other words, the toughness can be calibrated only under conditions where the hypothesis of continuum fails.