The linear thermoelastic problem of uniform heat flow disturbed by a two-dimensional crack in a strip

Under the assumption of plane strain, a solution for a thermoelastic problem concerning a strip is obtained by the method of dual integral equations. It is assumed that the crack is parallel to the edges of the strip. The variation with the strip width of stress-intensity factor is shown graphically.     

A thermoelastic contact problem on strip bending with allowance for thickness deformability

The bending of a strip on a heated half-space is considered on the assumption that the strip deforms in response to the temperature distribution and the force of a distributed load.     

The linear steady thermoelastic problem for a strip with a collinear array of Griffith cracks parallel to its edges

The problem of determining the thermal stresses when a uniform heat flow in a thermoelastic strip is disturbed by a collinear array of cracks is discussed. The solution of the Duhamel-Neumann equations is posed in terms of harmonic functions, which leads to dual series relations whose solutions are known. Numerical results for the stress intensity factors at the crack tips are displayed in graphical form.     

Steady thermal contact of a half strip and a strip

The steady temperature field of a strip and a half strip connected at one end but with different thermophysical properties is determined for mixed conditions in the contact region.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 2, pp. 302–307, August, 1987.     

Determining thermoelastic stresses in a plate

A method for approximate determination of thermoelastic stresses in an infinite plate is presented. With minimal complication of the problem, the proposed method yields results that deviate from the exact solutions within the limits of computational accuracy.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol.17, No. 2, pp. 350–353, August, 1969.     

Longitudinal thermoelastic bending of a flexible rod

Thermoelastic longitudinal bending of a flexible rod whose ends are secured in immovable hinged supports is considered. It is assumed that temperature is uniformly distributed along the rod and that it increases monotonically. This problem is solved for the case of large displacements. Support reaction, deflection, and rod length in relation to temperature in the post-critical condition are calculated.Translated from Problemy Prochnosti, No. 3, pp. 54–58, March, 1991.     

Edge waves in a thermoelastic plate

Temperature-rate-dependent thermoelasticity theory is employed to study waves propagating along the edges of a thin flat plate of infinite length, which is in a state of plane stress. Governing equations of the plane stress problem are derived and it is found that the speed of heat waves in this problem is, in general, less than that in the plane strain and the general three-dimensional problems. The waves of the desired type are analysed for isothermal and insulated edge conditions, and the paths of particles as well as the cut-off frequencies are determined. Waves in a thin bar and in a semi-infinite plate are discussed as limiting cases. The effects of the finiteness of the neat propagation speed are analysed in some detail.     

Fracture in quasi-brittle materials: a review of continuum damage-based approaches

Starting from the early ideas on smeared-crack modelling of quasi-brittle materials (concrete, rock) as pioneered in the late 1960s various refinements are discussed such as the shear retention factor, the tension-stiffening concept and the tension-softening concept. Next, smeared-crack models are put in the unified context of damage mechanics together with the multiple-smeared crack approach and the (closely) related microplane damage models. The concept of fracture energy is introduced for tensile and compressive loadings and is also elaborated for reinforced concrete. A concise summary is given of recent finite element concepts for cohesive-zone models (fracture energy models).     

Coupled thermoelastic vibrations of a Timoshenko beam

In the present paper we deal with tne dynamic behaviour of a Timoshenko beam subjected to a step heat flux to the surface z = + h/2 at time t = 0⁺. The mathematical analysis is based on integral transforms, the Muller's method of solving algebraic equations and the Heaviside expansion theorem. From the numericad results presented, one can see the effect of inertia and that of tne coupling between temperature and strain fields on the dynamic behaviour of the beam as well as the distribution of the temperature fields with time.     

Nominal strength of quasi-brittle open hole specimens

The relation between the nominal strength of open hole specimens manufactured with quasi-brittle isotropic materials with respect to the specimen size and the shape of the cohesive law is examined in the present paper. The obtained results can be used by engineers as design charts or to obtain valuable information on the failure characteristics of quasi-brittle materials.     

J-resistance curve and ductile tearing of a mild steel

The onset of ductile tearing at room temperature of mild steel BS 15 was studied using side grooved compact tension specimens. The approach to this problem was divided conveniently into two basic parts: first, identification and evaluation of the toughness at initiation of crack extension, and second, assessment and characterization of the subsequent crack growth behaviour. The critical value of the J integral for crack initiation, J_c was obtained using two different techniques: the multispecimen method and a single specimen compliance test. It was found that the latter could be used with much larger unloading than originally proposed. This has the advantage of greater accuracy in the determination of the compliance, and consequently in the evaluation of crack extension. In the second part of the work, resistance curves were obtained applying two different approaches. The resistance curves obtained following the more exact method were used for the determination of the tearing modulus T of the material, and the values thus derived, compared with a selection of other steels.     

Basic singular thermoelastic solutions for a crack

Basic, singular solutions of plane thermoelasticity for an infinite medium with a crack are studied and furnished in this article. By these solutions, thermal stresses and thermal stress intensity factors in the cracked medium, under the action of a point thermal inclusion or a point heat source, can simply and exactly be evaluated. These solutions are obtained by the use of the complex function method and some quadrature techniques. In the case of a heat source, exact expressions for the temperature distribution are also derived, and some dislocation solutions are employed to obtain the final expressions for thermal stresses and thermal stress intensity factors. A number of definite integrals, with logarithmic functions as main components in their integrands, have been treated rigorously to obtain exact and closed form formulas of evaluation. This kind of definite integral is characteristic in the thermoelastic analysis of cracked bodies. Numerical values for stress intensity factors and temperature distributions are worked out and presented in tabular or graphic form.     

Flutter of a viscoelastic strip

An approximate solution of the problem of flutter of a cantilever clamped viscoelastic strip is obtained under conditions where the flow velocity vector is parallel to the plane of the strip and forms an angle with its edges, which can take arbitrary values. The approximate solution in all the cases is based on the linear combinations of polynomials, which satisfy the boundary conditions. Approximate estimates of the values of the critical flutter speed are obtained by using the Laplace transform in time and a Galerkin expansion for the spatial structures. The nature of the changes in the critical speed with respect to the value of the angle of flow is examined. It is shown that for any non-negative angle of flow with increasing velocity of flow there is an instability in the form of flutter. For negative angles of the flow, either flutter or a cylindrical bending of the strip is observed. Principally, a new mechanical effect is found: there is a whole sector of directions for which increase in flow rate leads to a cylindrical bending.     

Analysis of ductile tearing using a local approach to fracture

In this paper, the Rice and Tracey (RT) model based on growth of cavities is verified in order to describe the ductile tearing in stainless steel 12Ni6Cr and aluminium alloy. Experimentally, central crack panel and compact tension specimens were tested. The comparison of the experimental results with the classical RT model shows that this model cannot make a good prediction using J −Δ a curve. On the basis of fitting procedure and numerical simulations, we have proposed a modification of this model by introducing corrective coefficients to improve the classical RT model. The proposed model, although very simple, is able to approximate with good accuracy the experimental results and that the approximation is, as expected, better than using the RT approach directly.     

J andG canalysis of the tearing of a highly ductile polymer

The use of a conventionalJ analysis to describe the ductile tearing of thin low density polyethylene sheet is described. This is a measure of the total energy required to cause fracture. The use of the current energy release rate to determine the local dissipation rate is then given and it is shown that an initiation (plane strain) and reasonably constant propagation (plane stress) values are obtained. Input energy of system - A Area of specimen - B Thickness of specimen - W Width of specimen - a Crack length - J J-integral - G _c Energy release rate - P Load - U Energy - C Compliance - M Constraint factor - _y Yield stress - u Displacement - Dimensionless factor     

On multiplicity of solutions in quasi-brittle fracture computations

The analysis of quasi-brittle fracture processes is formulated as a linear complementarity problem either in finite increments or in rates. Some time-stepping solution procedures and mathematical programming algorithms are discussed as for their ability to capture the whole set of possible alternative equilibrium paths. Potentialities and limitations of the proposed approach and of the relevant procedures are pointed out also by means of a numerical example.     

Calculation of thermoelastic stresses in a rectangular heated ingot

Thermoelastic stresses in a heated ingot are determined by the finite-difference method. We present the principal results of the numerical analysis. Dneprodzerzhinsk State Technical University, Dneprodzerzhinsk, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 130–136, July–August, 1997.