Photoelastic experimental hybrid method for fracture mechanics of anisotropic materials

In this paper, the isotropic and anisotropic photoelastic experimental hybrid methods for fracture mechanics are developed. Using the photoelastic experimental hybrid method, it is demonstrated that one can precisely obtain stress intensity factors and separate the stress components of isotropic and anisotropic plate problems from the only isochromatics.     

Stress Wave Field Near a Notched Boundary in Anisotropic Plates under Impulsive Loading

The stress distribution near a rectilinear boundary and a boundary with a notch of different depths in an anisotropic plate is analyzed. The plate boundary is under the action of a surface or embedded impulsive source. The results presented have been obtained using the dynamic photoelastic method for optically sensitive orthotropic plates. The results for orthotropic and isotropic plates with different ratios of notch depth to wavelength are analyzed     

Photoelastic stress analysis of orthtropic materials by using an isotropic plate

Based on the two-dimensional theory of elasticity for an orthotropic plate, relations between stress components produced in two different orthotropic plates are considered and the conditions to realize the similar stress fields in different orthotropic plates are studied. On the basis of the similarity law, a convenient photoelastic method to analyze stress fields in an orthotropic plate, using an isotropic plate, is presented. Two examples are treated. One deals with the stress-concentration problem around a circular hole in a strip with edges parallel to the symmetric axis of elasticity. In the second example, the edges of the strip are assumed to be inclined by 30 deg to the elastically symmetric axes. The experimental results are compared with theoretical calculations. Paper was presented at the SEM VII International Congress on Experimental Mechanics held in Las Vegas, NV on June 8–11, 1992.     

Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

The paper sets forth a photoelastic method for the determination of the dynamic stress concentration factor near a hole in an orthotropic plate. The stress distribution at the periphery of a circular hole is analyzed. The stress concentration factors for orthotropic and isotropic plates under dynamic and statical loading are compared     

Near-Boundary Stress Wave Field in Anisotropic Plates under Impulsive Load

The stress wave field and the behavior of waves near the free boundary in an orthotropic plate and at the interface between two anisotropic media are studied. The results presented were obtained using the dynamic photoelastic method and optically sensitive fibrous models. Experimental data for impulsively loaded plates with various boundary conditions are analyzed     

A stress-optic law for photoelastic analysis of orthotropic composites

The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress. Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.     

复合材料光弹性分析的工程方法

本文在推导均衡光弹性复合材料应力(应变)—光定律的基础上,导出了均衡光弹性复合材料的近似应变—光定律。然后加以推广,提出适用于一般光弹性复合材料的近似应变—光定律.精度分析及实验验证表明:作为工程计算,在采用本文推荐的参数时,光弹性复合材料可视作各向同性材料进行光弹性分析。     

Solution of nonstationary problems in the mechanics of anisotropic bodies by the method of dynamic photoelasticity

The results obtained in developing and applying the method of dynamic photoelasticity to two-dimensional problems in the mechanics of anisotropic bodies are reviewed. The theory behind the method and its engineering implementation are described. The capabilities of the method are illustrated by solving specific nonstationary problems: dynamic stress concentration, diffraction of longitudinal and transverse waves by free and reinforced holes, dynamic fracture of orthotropic plates with holes and cracks under impulsive and explosive loads     

各向异性板的面导纳特性研究

目前在工程上各向异性结构中的振动问题和振动能量传递的问题越来越多,然而对各向异性结构导纳的研究还不充分,对各向异性板面导纳的研究也还处于萌芽状态.面导纳不仅反映结构的振动特性还能反映能量传递的特性,因此面导纳比点导纳在工程上更加贴合实际.论文根据理论公式获得了一般各向异性板面导纳的理论解,并与有限元模型的数值解对比发现...     

Oblique edge crack in an anisotropic material under antiplane shear

An oblique edge crack in an anisotropic material under antiplane shear loadings is investigated. The antiplane problems are formulated based on a linear transformation method. An anisotropic solid containing an edge crack subjected to concentrated forces is first considered. The stress intensity factor for the edge crack with concentrated forces is obtained from the solution of the transformed edge crack in an isotropic material which is solved by using conformal mapping technique and complex function theory. The solution of the edge crack under concentrated loads is used to construct the stress intensity factor for the oblique edge crack in the anisotropic material subjected to antiplane distributed loads. Some numerical computations are carried out to calculate the stress intensity factors for the edge crack in inclined orthotropic materials subjected to point forces as well as distributed tractions.     

复合材料光弹性分析的近似方法

本文提出了一种用于光弹性复合材料的简化应变——光学定律。按照这一简化定律。模型材料的主应变差和主应变方向只要利用光弹性实验测出的等差线与等倾线即可求得。些是一种正交异性光弹性分析的近似方法,这一方法所得结果与实验数据比较,最大误差在10％左右。由于采用简化应变——光学定律使得正交异性光弹性分析工作大为简便,因此它是一种适合于工程应用的近似方法。     

Stress intensity factor for a kinked interfacial crack in dissimilar anisotropic materials under antiplane deformation

The asymptotic problem of a kinked interfacial crack in dissimilar anisotropic materials under antiplane deformation is investigated. The linear transformation method for the problem of the anisotropic bimaterial with a straight interface is proposed. The stress intensity factor for the kinked interfacial crack in the anisotropic composite is obtained from the solution of the transformed problem of the kinked interfacial crack in the isotropic bimaterial based on the linear transformation method. The effects of the material parameters as well as the kink angle on the stress intensity factor are discussed from numerical results of the stress intensity factor. The finite element analysis is carried out to verify the stress intensity factor obtained by using the linear transformation. The influence of the material orientations on the stress intensity factor is investigated for the kinked crack in the bimaterial consisting of dissimilar inclined orthotropic materials.     

Natural frequencies of thin,rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh–Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or “patch”, carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.     

光弹法实测正交异性双材料界面裂纹断裂参数

采用光弹贴片法实测正交异性双材料界面裂纹尖端区域的应力应变场, 进而求出界面裂纹的断裂力学参量. 将正交异性双材料板加工成拉伸试件,在聚碳酸酯贴片 的单侧表面镀金属铝膜,以提高贴片的反射效率. 沿贴片后的双材料界面预制裂缝,逐渐加 大载荷,得到一系列清晰的等差线条纹图. 利用正交异性双材料界面裂纹尖端应力分量表达 式计算出应力强度因子. 实验表明,光弹贴片法可有效地分析正交异性双材料界面裂纹问题.     

Affine transformations of the equations of the linear theory of elasticity

This paper deals with the general formulas of affine transformations that preserve invariance of the static equations of the linear theory of elasticity in the case of arbitrary anisotropic materials. The invariance of the equations with respect to affine transformations allows one to model a given anisotropic material by another material. All anisotropic materials are divided into classes of mutually congruent materials. The congruency conditions are obtained for orthotropic and isotropic materials and for orthotropic and transversely isotropic materials. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 124–134, July–August, 2006.     

Anisotropy tensor of the potential model of steady creep

The Kelvin approach describing the structure of the generalized Hooke’s law is used to analyze the potential model of anisotropic creep of materials. The creep equations of incompressible transversely isotropic, orthotropic materials and those with cubic symmetry are considered. The eigen coefficients of anisotropy and eigen tensors for the anisotropy tensors of these materials are determined.     

Elastic characterization of anisotropic materials by speckle interferometry

In this paper we present an experimental procedure for the elastic characterization of thin anisotropic plates. The procedure allows the determination of the elastic constants of isotropic materials (metals and ceramics) and orthotropic materials (composite laminae). Moreover, the flexural compliances of completely anisotropic uncoupled materials (most of composite laminates) can also be measured. The tests are carried out by applying a concentrated force to the specimen supported by three spheres. The stress components are evaluated by simply measuring the applied load, while the strain fields are measured by digital phase-shifting speckle interferometry. The experimental procedure is entirely controlled by a virtual instrument developed for this purpose in the National Instruments LabVIEW^® environment, which runs on a personal computer interfaced with a standard black and white CCD camera. By means of the speckle interferometer, the whole field of the out-of-plane displacements is acquired; the curvatures, and hence the strain components, are obtained by two subsequent numerical differentiations. The numerical processing of the experimental data was carried out in the Mathematica? environment. The results obtained on a steel specimen and on a composite laminate are reported.     

Transmission photoelasticity of centrally loaded generally and specially orthotropic beams

Transmission photoelastic patterns for generally and specially orthotropic beams and an isotropic beam are presented. Theoretical isochromatic and isoclinic results for these beams, calculated from classical elasticity stress equations and stress-optic laws, are also presented and compared with experiment. The agreement between the theory and experiment is excellent. For the orthotropic beams, a stressoptic law which accounts for the effects of residual birefringence was used. The residual birefringence observed for the composite used in this study is greater than one fringe order and results from a matrix residual tension which is about one fourth of the resin's ultimate tensile strength. Finally, the influence of such a large residual birefringence on beam and calibration photoelastic data is discussed in detail. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics, held in New Orleans, LA on June 8–13.     

End effects for plane deformations of an elastic anisotropic semi-infinite strip

In the linear theory of elasticity, Saint-Venant's principle is used to justify the neglect of edge effects when determining stresses in a body. For isotropic materials, the validity of this is well established. However for anisotropic and composite materials, experimental results have shown that edge effects may persist much farther into the material than for isotropic materials and as a result cannot be neglected. This paper further examines the effects of material anisotropy on the exponential decay rate for stresses in a semi-infinite elastic strip. A linearly elastic semi-infinite strip in a state of plane stress/strain subject to a self-equilibrated end load is considered first for a specially orthotropic material and then for the general anisotropic material. The problem is governed by a fourth-order elliptic partial differential equation with constant coefficients. In the former case, just a single dimensionless material parameter appears, while in the latter, only three dimensionless parameters are required. Energy methods are used to establish lower bounds on the actual stress decay rate. Both analytic and numerical estimates are obtained in terms of the elastic constants of the material and results are shown for several contemporary engineering materials. When compared with the exact stress decay rate computed numerically from the eigenvalues of a fourth-order ordinary differential equation, the results in some cases show a high degree of accuracy. In particular, for strongly orthotropic materials, an asymptotic estimate provides extremely accurate estimates for the decay rate. Results of the type obtained here have several important practical applications. For example, they provide physical insight into the mechanical testing of anisotropic and laminated composite structures (including the off-axis tension test), are useful in assessing the influence of fasteners, joints, etc. on the behavior of composite structures and allow for tailoring a material with specific properties to ensure that local stresses attenuate at a desired rate.     

Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids

It has been known for some time that certain radial anisotropies in some linear elasticity problems can give rise to stress singularities which are absent in the corresponding isotropic problems. Recently related issues were examined by other authors in the context of plane strain axisymmetric deformations of a hollow circular cylindrically anisotropic linearly elastic cylinder under uniform external pressure, an anisotropic analog of the classic isotropic Lamé problem. In the isotropic case, as the external radius increases, the stresses rapidly approach those for a traction-free cavity in an infinite medium under remotely applied uniform compression. However, it has been shown that this does not occur when the cylinder is even slightly anisotropic. In this paper, we provide further elaboration on these issues. For the externally pressurized hollow cylinder (or disk), it is shown that for radially orthotropic materials, the maximum hoop stress occurs always on the inner boundary (as in the isotropic case) but that the stress concentration factor is infinite. For circumferentially orthotropic materials, if the tube is sufficiently thin, the maximum hoop stress always occurs on the inner boundary whereas for sufficiently thick tubes, the maximum hoop stress occurs at the outer boundary. For the case of an internally pressurized tube, the anisotropic problem does not give rise to such radical differences in stress behavior from the isotropic problem. Such differences do, however, arise in the problem of an anisotropic disk, in plane stress, rotating at a constant angular velocity about its center, as well as in the three-dimensional problem governing radially symmetric deformations of anisotropic externally pressurized hollow spheres. The anisotropies of concern here do arise in technological applications such as the processing of fiber composites as well as the casting of metals.