Stress field near interface crack tip of double dissimilar orthotropic composite materials

In this paper, double dissimilar orthotropic composite materials interfacial crack is studied by constructing new stress functions and employing the method of composite material complex. When the characteristic equations＇ discriminants △1 〉 0 and △2 〉0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and interembedding between the interfaces of the crack.

Crack tip higher order stress fields for functionally graded materials with generalized form of gradation

A generalized form of material gradation applicable to a more broad range of functionally graded materials(FGMs) was presented.With the material model,analytical expressions of crack tip higher order stress fields in a series form for opening mode and shear mode cracks under quasi-static loading were developed through the approach of asymptotic analysis.Then,a numerical experiment was conducted to verify the accuracy of the developed expressions for representing crack tip stress fields and their validity in full field data analysis by using them to extract the stress intensity factors from the results of a finite element analysis by local collocation and then comparing the estimations with the existing solution.The expressions show that nonhomogeneity parameters are embedded in the angular functions associated with higher terms in a recursive manner and at least the first three terms in the expansions must be considered to explicitly account for material nonhomogeneity effects on crack tip stress fields in the case of FGMs.The numerical experiment further confirms that the addition of the nonhomogeneity specific terms in the expressions not only improves estimates of stress intensity factor,but also gives consistent estimates as the distance away from the crack tip increases.Hence,the analytical expressions are suitable for the representation of crack tip stress fields and the analysis of full field data.

EFFECT OF THE POISSON RATIO ON THE PERFECTLY PLASTIC STRESS FIELD AT A STATIONARY PLANE-STRAIN CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.

A WEIGHTED RESIDUAL METHOD FOR ELASTIC-PLASTIC ANALYSIS NEAR A CRACK TIP AND THE CALCULATION OF THE PLASTIC STRESS INTENSITY FACTORS

In this paper, a weighted residual method for the elastic-plastic analysis near a crack tip is systematically given by taking the model of power-law hardening under plane strain condition as a sample. The elastic-plastic solutions of the crack lip field and an approach based on the superposition of the nonlinear finite element method on the complete solution in the whole crack body field, to calculate the plastic stress intensity factors, are also developed. Therefore, a complete analvsis based on the calculation both for the crack tip field and for the whole crack body field is provided.

SUPPLEMENTARY STUDY ON ANISOTROPIC PLASTIC STRESS FIELDS AT A STATIONARY PLANE-STRESS CRACK-TIP

Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.

ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE-STRESS CRACK-TIP

Under the condition that all the stress components at a crack-tip are the functions of 0 only, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip. Applying this general solution to four particular cases of anisotropy, the general solutions of these four particular cases are derived. Finally, we give the anisotropic plastic field at the rapidly propagating plane-stress mode I crack-tip in the case of X=Y=Z

PERFECTLY PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE-STRESS CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of only, making use of the Mises yield condition , steady-state moving equations and elastic perfectly-plastic constitutive equations, we derive the generally analytical expressions of perfectly plastic fields at a rapidly propagating plane-stress crack tip. Applying these generally analytical expressions to the concrete crack, we obtain the analytical expressions of perfectly plastic fields at the rapidly propagating tips of modes I and II plane-stress cracks.

ANISOTROPIC PLASTIC STRESS FIELDS AT A SLOWLY PROPAGATING CRACK TIP

Under the condition that any perfeetly plastic stress components at a crack tip are nothing but the Junctions of 0 only, making use of equilibriumequations,Hill ani.sutropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastiestress Jields at the slowly steadyhe slowly steady propagatin tips of plane and anti-phane strain,Applying these general analytical expressions to the concrete cracks the attchvtical expressions of anisotropie plastic stress fields at the slowly steady propagating tips of Motle I and Motle III cracks are obtained. For the isolropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfeeby plastic mress fields

The Plane Stress Crack-Tip Field for an Incompressible Rubber Material

The crack-tip field under plane stress condition for an incompressible rubbermaterial￣[1] is investigated by. the use of the fully nonlinear equilibrium theory. It isfound thai the crack-tip field is composed of two shrink sectors and one expansion se-ctor. At the crack-tip, stress and strain possess the singularity of R￣(-1) and R￣(-1n), respec-tively, (R is the distance to the crack-tip before deformation, n is the material const-ant). When the crack-tip is approached, the thickness of the sheet shrinks to zerowith the order of R￣(1.4n). The results obtained in this paper are consistent with that ob-tained in [8] when s→∞ .

MODE Ⅰ CRACK TIP FIELD WITH STRAIN GRADIENT EFFECTS

A plane strain mode 1 crack tip field with strain gradient effects is investigated.A new strain gradient theory is used.An elastic-power law hardening strain gradient material is considered and two hardening laws,i.e.a separation law and an integration law are used respectively.As for the material with the separation law hardening,the angular distributions of stresses are consistent with the HRR field,which differs from the stress results;the angular distributions of couple stresses are the same as the couple stress results.For the material with the integration law hardening,the stress field and the couple stress field can not exist simultaneously,which is the same as the conclusion,but for the stress dominated field,the an- gular distributions of stresses are consistent with the HRR field;for the couple stress dominated field,the an- gular distributions of couple stresses are consistent with those in Ref.However,the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only,while the crack tip field of mode 1 is dominated by the tension gradient,which will be shown in another paper.

MODE Ⅰ AND MODE Ⅱ CRACK TIP ASYMPTOTIC FIELDS WITH STRAIN GRADIENT EFFECTS

The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

ANALYSIS OF ENERGY RELEASE RATE FOR CRACKED LAMINATES

An interface crack analysis is presented for further understanding the characteristics of the crack-tip field. The conditions under which the energy release rate components would exist are emphasized and the relations between energy release rate components and the stress intensity factors are given. Combining with the results of chasical plate theory analysis. a closed-form solution for stress intensity factors in terms of external loading as well as some geometric and material parameters for fairly general composite laminates is derived Then. an analytical solution for energy release rate components is deduced. In order to get energy release rate components under general loading condition. a mode mix parameter, Ω, must be determined separately. A methodology for determining Ω is discussed. Finally. several different kinds of laminates are examined and the results obtained could be used in engineering applications.

孔洞对疲劳裂纹扩展路径的影响

为了研究孔洞位置和尺寸对疲劳裂纹扩展路径的影响,利用ABAQUS有限元仿真软件建立改进CT试样的裂纹扩展仿真模型,采用扩展有限元法研究了在低周疲劳加载条件下Q235钢圆孔与裂纹尖端的角度、距离以及圆孔半径对裂纹扩展路径的影响,并通过引入裂纹偏转系数来定量描述不同参数对裂纹扩展路径偏转程度的影响。结果表明:当圆孔与裂纹尖端的夹角为45°时,裂纹偏转系数取得最大值;裂纹偏转系数随着孔洞半径的增加逐渐增大,随着圆孔与裂纹尖端距离的增大逐渐减小。

正交异性双材料界面裂纹尖端应力场

通过构造新的应力函数,利用复合材料断裂复变方法,对正交异性双材料界面裂纹进行了研究.在特征方程组的判别式都大于零的情形下,推出了Ⅰ型界面裂纹尖端的应力场、位移场的理论公式,其结果没有振荡奇异性及裂纹面没有相互嵌入现象。

单边裂纹通电瞬间裂尖处应力场的复变函数解

本文应用复变函数中的Schwarz-Christoffel变换方法,在具单边裂纹的导电薄板通电瞬间温度场复变函数解的基础上,推导出用复变函数表示的应力场的表达式,并且给出算例。通过理论计算得知:当对具有单边裂纹的导电薄板通入适当密度的电流时,裂尖处温度急剧升高并熔化使裂尖变钝。同时,在裂尖周围形成了有利于遏制裂纹扩展的压应力场,有效地防止了裂纹沿其主方向和其它方向延伸。从理论上证明了电磁热效应在裂尖处产生高温形成焊口的同时,压应力场的形成是遏制裂纹扩展的主要因素之一。理论计算结果与实验结果比较吻合,为这一止裂方法的应用打下了理论基础。

预测疲劳裂纹扩展的多种理论模型研究

大多数工程断裂是因疲劳而引起的,所以金属材料的低周疲劳和裂纹扩展速率性能一直受到安全设计部门的关注。长久以来,国内外学者在建立金属材料低周疲劳行为和裂纹扩展速率性能之间的关系方面进行了多材料和多角度的研究。基于平面应力裂纹尖端小范围屈服应力应变场和疲劳裂纹扩展失效准则,提出用于I型疲劳裂纹扩展速率的预测模型。针对国内外相关工作的研究,基于平面应力裂纹尖端小范围屈服应力应变场和疲劳裂纹尖端循环塑性区内的应变能失效准则,提出一个可用于I型疲劳裂纹扩展速率的预测模型。借助已发表的15种金属材料对应的低周疲劳和裂纹扩展速率性能数据,详细分析和比较所提出的预测模型与其他6种预测模型的预测规律和结果。研究表明,所提出的预测模型能够预测更广泛的金属材料疲劳裂纹扩展速率,并且较其他6中预测模型更符合安全设计的理念。

直接计算应力强度因子的扩展有限元法

系统地给出了直接计算应力强度因子的扩展有限元法。该方法以常规有限元法为基础,利用单位分解法思想,通过在近似位移表达式中增加能够反映裂纹面的不连续函数及反映裂尖局部特性的裂尖渐进位移场函数,间接体现裂纹面的存在,从而无需使裂纹面与有限元网格一致,无需在裂尖布置高密度网格,也不需要后处理就可以直接计算出应力强度因子,并且大大简化了前后处理工作。最后通过两个简单算例验证了该方法的精度,分析了影响计算结果的因素,并与采用J积分计算的应力强度因子作了对比,得出了两种方法计算精度相当的结论。

含缺口受拉平板塑性应力场的有限元分析

含尖缺口受拉平板三维应力场是断裂分析研究中常遇到的问题,进入塑性状态以后,缺口尖端的应力状态和分布与弹性条件下有很大的不同。通过有限元的方法对含缺口受拉平板的塑性应力场进行了分析,并进一步研究了厚度和缺口半径因素对缺口尖端应力场的影响。分析结果表明,缺口半径减小提高了平面内应力σx和σy,也提高厚度方向应力σz和平面应变系数,平面应变系数在塑性条件下趋于0.5;厚度对平面内应力σx和σy影响很小,但提高厚度方向应力σz和平面应变系数,平面应变系数在载荷较小时趋于材料泊松比μ,在载荷较大时趋于0.5。

双材料高聚物界面断裂行为的实验研究

将数字相关图象测量方法和显微技术结合起来 ,实现了物体表面位移和应变的细观测量。应用这一方法 ,对双材料高聚物界面断裂行为进行了实验研究 ,定量测量了具有界面裂纹受剪切载荷作用的双材料试件的裂尖附近微小区域内的位移和应变。最后对实验结果进行了分析和讨论 。

纯扭正交异性复合材料板的断裂分析

对受纯扭载荷作用的线弹性正交异性复合材料板裂纹尖端附近的断裂性态进行探讨 .利用复变函数方法 ,通过求解偏微分方程的边值问题 ,推出了裂纹尖端附近的弯矩、扭矩、应力和位移的表达式 。