Since the motion of individual microelements can be expressed theoretically and since experimental observations are usually evaluated in terms of macroscopic quantities, a connection between the two descriptions becomes necessary in solid mechanics. For this purpose mesomechanics is introduced which is based on the notion of an intermediary domain referred to as a mesodomain. The mesodomain is interpreted as a volume that is much smaller than the macroscopic domain of the entire body but much larger than the microscopic domain of the material. Constitutive equations are widely studied mesoscopically. Moreover, the new balance equations are required and consequently, the field equations are revised to describe the precise behavior of the mesoscopic structure of materials.
Thermoelastic stress analysis(TSA) is a technique for measuring stresses through temperature changes induced by the thermoelastic effect of elastic bodies. Since the TSA can only provide the sum of the principal stresses, stress separation is required to obtain individual stress components. This paper deals with stress separation of TSA data. The problem is divided into two: (1)an inverse problem to estimate the unknown boundary values from the sum of the principal stresses inside the body, and (2)a direct problem to derive the stress components inside the body on the basis of the estimated boundary values. This two-step method can be applied to a wide range of practical problems if both the inverse and direct problems are solved by FEM or BEM. In this study, the problem is formulated by BEM. It is shown that careful treatment of the inverse problem is essential for attaining an accurate result of the stress separation. The combination of the truncated singular value decomposition and Hansen's L-curve method is found to be effective for the purpose.
In this study, the one-dimensional transient thermal stress problem of a non-homogeneous hollow circular cylinder with arbitrarily distributed and continuously varied material properties, such as functionally graded materials, is evaluated theoretically. Using the analytical procedure of a laminated hollow circular cylinder model, the analytical temperature solution for the cylinder is derived approximately. Furthermore, making use of Airy's stress function method, the thermal stress components are formulated under the mechanical condition of being traction-free. As a numerical example, a hollow circular cylinder composed of zirconium oxide(ZrO2)and titanium alloy(Ti-6Al-4V)is considered. To optimize(i.e., minimize) the thermal stress distribution, numerical calculations are carried out, and the optimum material composition is determined taking into account the effect of the temperaturedependence of the material properties. Furthermore, taking into account the variation in the thickness of the cylinder, the temperature rise of the surrounding medium, and the relative heat transfer coefficients on the inner and outer surfaces, the optimum values of the material composition are obtained. Numerical data for the calculations are shown graphically.
A numerical analysis of two-dimensional wave propagation in a transversely isotropic cylinder is presented. The equations governing the dynamic deformation are solved by means of the method of numerical integration along bicharacteristics. Numerical simulations of elastic wave propagation in a fiber-reinforced composite cylinder due to impact load are performed. A numerical solution for the special case of the transversely isotropic cylinder is shown to be in acceptable agreement with impact experiment results. The stability and convergence of the present method are evaluated by checking the relative error in the total energy of the system.
Various stresses were applied to specimens prepared from silicon carbide and cold-rolled stainless steel, JIS type SUS 304, and the changes in peak positions of a diffraction line on a sin2ψ diagram were investigated for x-ray diffraction measurement of residual stress of textured materials. Seven peak positions of a diffraction line measured at different ψ angles for each applied stress oscillated in a sin2ψ diagram. However, the slope M and the intercept N of a straight line fitted to the seven peak positions varied linearly with the applied stress σ0. It is confirmed analytically and experimentally that these experimental findings show that the lattice strain for a fixed ψ angle varies linearly with applied stress as is the case with isotropic materials. Therefore, the stress constant K of textured materials can be determined experimentally as the reciprocal of the slope of the straight line in the M-σ0 diagram.
We have developed an optical equipment that possesses high detection sensitivity for measuring the small optical retardation induced by small stress by means of laser photoelasticity. A He-Ne laser is used as a light source to measure small stress in transparent materials. We explain the theory and process of the measurement of optical retardation in the materials. The magnitudes of principal stress difference and the directions of the principal stress are obtained simultaneously and quantitatively using our equipment. To evaluate the validity of the measurement results of the equipment, the stress distribution of a pulled rectangular glass plate with notches at both sides is measured using the equipment. The experimental results of stress distribution agree well with the analytical results of FEM. The stress distribution can be determined quickly by using the equipment and scanning stress distribution measurement has been realized.
A simple FEM model of fibers used to reinforce materials is proposed which is very effective at saving computational time. By making use of this model, deformation behaviors of fiber-reinforced materials subjected to tension are investigated especially in the large plastic strain range, in which four kinds of typical regular arrangement of fibers and one random arrangement are adopted. The reinforcing effect of fibers is not found necessarily to be parallel to the stabilizing effect of plastic flow, according to various conditions such as fiber-arrangement, the volume fraction of fibers and boundary conditions. Attention is thus mainly directed to the unstable aspect of plastic deformation, yielding recommendations for fiber-arrangements with respect to the soundness of the plastic behavior of fiber-reinforced materials.
A two-dimensional finite element model of an elastic-plastic solid(aluminum)is used to predict the plastic properties including stress-strain behaviour of aluminum composites containing up to 40 volume percent particulate reinforcements under combined loading up to 0.2 in equivalent logarithmic strain. The effects of reinforcement size, shape, contents, orientation, elastic properties and loading conditions on the overall behavior of the composite are investigated. The elastic modulus of the composites is isotropic, almost independent of the type of reinforcement, and controlled solely by the volume percentage of reinforcement present. The work hardening exponent of the composites(one of the plastic properties)is surprisingly influenced by the ratio(γ)of the elastic constants of the reinforcement and the matrix in an inverse manner. It is also affected by the volume fraction, size, shape, orientation and distribution of the reinforcement. The variation in flow stress is controlled primarily by volume fraction, type, distribution and γ. For various loading conditions, the parameters, namely, the work hardening exponent, elastic modulus and flow stress of the composites for all kinds of reinforcements, remain almost constant for a particular value of γ and volume fraction with a slight change in the values for plane strain tension. For porous solids, these parameters are affected slightly by the loading conditions. Furthermore, the degree of constitutive softening of porous solids is strongly dependent on the volume fraction and shape of voids. A comparison of properties with conventional aluminum shows that an improvement in the plastic properety of a metal by combination with other metals could become an interesting subject, especially in the field of metal forming processes. For such research, the FEM model used here is a powerful tool.
We previously proposed a constitutive expression of plastic deformation which can incorporate the directional dependence of the plastic strain increment εP on the stress increment σ. The expression was given in terms of two transition parameters μ(α) and β(α) which denote the magnitude and the direction angle of the plastic increment, where α denotes the direction angle of the stress increment measured from a particular direction, termed "natural direction", in which the direction of the stress increment coincides with that of the plastic strain increment. The expression can be utilized once we obtain the parameters μ(α) and β(α) through experimentation on industrial materials and/or theoretical studies such as polycrystalline model analyses. In this report, a computer code for a finite-element polycrystalline model is developed and used for the investigation of the variations of the two constitutive parameters μ(α) and β(α).
A model of cleavage fracture in granular bainite was developed. It involves two-dimensional elastic interaction between a main crack and multiple microcracks induced by the existence of martensite-austenite(M-A) particles in front of the main crack. A factor of fracture toughness reduction due to the presence of M-A particles(f(MA))was introduced to describe the effect of M-A particles on the stress intensity factor at the tip of the main crack. The values of f(MA)can be expressed as the inverse of the amplification coefficient of the stress intensity factor as a result from the interference between microcracks and a main crack in brittle materials. An equation was derived which describes the relationship between fracture toughness and microstructural variables, including the influence of the effective grain size as well as the average width and interspacing of M-A particles. Moreover, simple linear regression equations were used to check the validation of the present model for predicting cleavage fracture toughness in simulated coarse-grained heat-affected zones of quenched and tempered high-strength low-alloyed steels.
In this study, we employ the ordinary differential constitutive equations of endochronic theory to investigate the collapse of a thin-walled tube subjected to bending. A virtual work approach is used to formulate the problem, which results in a set of nonlinear algebraic equations that are numerically solved. Experimental data on a 6061-T6 aluminum alloy under cyclic bending and 304 stainless steel under combined bending and external pressure found in previous literature are compared with the theoretical simulation. The experimental and theoretical results are in good agreement. Finally, by using the rate-sensitivity function of the intrinsic time measure in the theory, the theoretical analysis is extended to investigate the viscoplastic collapse of a thin-walled tube subjected to bending. Owing to the hardening of the metal tube for a faster curvature rate, the magnitude of the limit moment, the ovalization of the tube cross section and the value of curvature at collapse are theoretically demonstrated to have increased.