The stability of crack growth in a beam subject to combined bending and tensile loadings: I: Beam built-in at one end

The stability of crack growth in a beam subject to combined bending and tensile loadings is examined for the case where the material is very ductile and where the beam is built-in at one end. Application of a displacement at the free end, and variation of the angle which the displacement makes with the beam, allows the combined effects of bending and tensile loadings on the stability of crack growth to be assessed. The stability analysis is based on the tearing modulus procedure, and the general conclusion is that tensile loadings can promote crack instability.     

The stability of crack growth in a beam subject to combined bending and tensile loadings. II: Beam subject to rotations and lateral displacements at the ends

The stability of crack growth in a beam subject to combined bending and tensile loadings is examined for the case where the material is very ductile and where the beam is built-in at one end. Application of a displacement at the free end, and variation of the angle which the displacement makes with the beam, allows the combined effects of bending and tensile loadings on the stability of crack growth to be assessed. The stability analysis is based on the tearing modulus procedure, and the general conclusion is that tensile loadings can promote crack instability.     

The effect of non-uniform bending deformation on the stability of circumferential growth of through-wall cracks in brass tubes

Experimental results on the stability of circumferential growth of through-wall cracks in brass tubes, show that non-uniform bending can adversely affect the crack stability criterion. The results are relevant to the important technological problem of crack stability in 304 stainless steel pipes used in Boiling Water Reactors.     

组合荷载作用下腐蚀缺陷管道的极限承载力

腐蚀缺陷的存在会降低管道的承载力,影响管道的正常运行.考虑了管道轴向与环向材料强度的各向异性,提出了腐蚀缺陷压力管道在内压、轴力和弯矩组合荷载作用下极限承载力的一组广义解.推导了等深度腐蚀、椭圆腐蚀和抛物线三种形状腐蚀缺陷管道的解析解.通过算例验证了解析解与广义解结果具有很好的吻合性.腐蚀形状对极限承载力有显著影响,把...     

The viability of a simple procedure for determining the criterion for the instability of circumferential growth of a through-wall crack in a stainless steel piping system, Part 2: The applied displacements produce bending and tensile deformation

Against the background of the technological problem of integranular stress corrosion cracking of Type 304 stainless steel Boiling Water Reactor piping systems, the stability of a circumferential through-wall crack is examined, for the case where the cracked section is at a position where the pipe enters a larger component. The paper presents a general methodology for determining the instability criterion for fixed displacement loadings, which are appropriate for an accident condition, the criterion being expressed in terms of the applied and material tearing moduli, or equivalently in terms of an effective pipe length. The methodology is applied to models which simulate bends in a piping system, and general conclusions are drawn with regards to the effect of pipe bends on crack instability.     

The stability of a circumferential crack in a pipe II. A simple procedure for determining the effective pipe length

A simple procedure is currently used to determine the effective pipe length associated with the instability of circumferential crack growth in a piping system. This procedure involves a separation of the complete piping system into two elastic parts at the cracked cross-section, the application of equal and opposite moments M to the cut faces, and the equation of the effective pipe length with $\text{El∥φ∥}\text{M}$ where φ is the rotational discontinuity generated at this section, E is Young's modulus and I is the second moment of area of the pipe at the cracked section. It is presumed that the pipe-ends remain fixed, i.e. they are built-in, throughout this operation. This paper shows that this procedure refers to the stability of a crack in a piping system which is subject to either a fixed displacement or a fixed rotation at a built-in end. The viability of the simple procedure is therefore underscored by the present paper's analysis.     

The stability of a circumferential crack in a pipe I. The influence of the boundary conditions imposed at the ends

The paper examines the case where a pipe of length L is built-in at one end and the other end is subject to an imposed displacement or rotation. The criterion for instability of growth of a circumferential through-wall crack is shown to depend on the pipe-end boundary conditions as well as the pipe geometry, crack size and crack location. The worst possible case is that where there is only a force, but no moment, at the pipe-end. However, this is probably an artificial situation which is unlikely to arise in practice. A pipe is more likely to be built-in at both ends, and for this situation, it is concluded that the instability criterion is the same irrespective of whether a displacement or rotation is imposed at a built-in end.     

The viability of a simple procedure for determining the criterion for the instability of circumferential growth of a through-wall crack in a stainless steel piping system,Part 1: The applied displacements produce only bending deformation

This paper investigates the stability of a circumferential through-wall crack in a straight segment of stainless steel pipe which is built-in at both ends. One built-in end is fixed, while the other is subject to both a rotation and a transverse displacement. In analysing this situation, it is assumed that the material is non-work-hardening, with plasticity being confined to the cracked cross-section which is fully yielded; the remainder of the pipe deforms elastically. The plasticity is in the form of a rotation about a neutral axis, but allowance is made for the axial displacement produced by this rotation, and in this respect the analysis is an improvement upon some earlier analyses. The instability criterion, obtained with the aid of the tearing modulus methodology, is shown to be independent of the details of the imposed boundary conditions, but it is different to the criterion obtained by ignoring the axial displacement. The paper discusses the implications of the results to the problem of crack instability in stainless steel nuclear reactor piping systems, particularly with regards to the viability of a simple procedure that is currently used to assess the integrity of piping systems.     

Analysis of dynamic growth of a tensile crack in an elastic-plastic material

The influence of inertia on the stress and deformation fields near the tip of a crack growing in an elastic-plastic material is studied. The material is characterized by the von Mises yield criterion and J₂ flow theory of plasticity. The crack grows steadily under plane strain conditions in the tensile opening mode. Features of the stress and deformation state at points near the moving crack tip are described for elastic-perfectly plastic response and for several crack propagation speeds. It is found that inertia has a significant effect on the elastic-plastic response of material particles near the crack tip, and that elastic unloading may occur behind the crack tip for higher speeds. The relationship between the applied crack driving force, represented by a remote stress intensity factor, and the crack tip speed is examined on the basis of a critical crack tip opening angle growth criterion. The calculated result is compared with dynamic fracture toughness versus crack speed data for a 4340 steel.     

Large deflections of a beam subject to three-point bending

In this paper, a solution for the equilibrium configuration of an elastic beam subject to three-point bending is given in terms of Jacobi elliptical functions. General equations are derived, and the domain of the solution is established. Several examples that illustrate a use of the solution are discussed. The obtained numerical results are compared with the results of other authors. An approximation formula by which the beam load is given as a polynomial function of beam deflection is also derived. The range of applicability of the approximation is illustrated by numerical examples.     

Hardening of a rolled sheet submitted to radial and complex biaxial tensile loadings

Biaxial tensile tests are performed on cruciform specimens with the help of direct biaxial testing machine. Small offset-strain yield curves are detected on an aluminium alloy (AL1200) rolled sheet submitted to irreversible radial and complex biaxial tensile loadings. A predominant kinematic hardening and an important isotropic expansion are observed. A yield curve distortion is observed as well but, unlike the traction–torsion case, its intensity appears to be linked to the loading type. Moreover, the strain responses are analyzed in order to point out the pronounced anisotropy of the rolled sheet and to check if the sheet behavior is in agreement with a plastic flow associated with the yield curve.     

Investigation of the crack problem in non-local piezoelectric materials under combined electromechanical loadings

The present investigation of the crack problem in piezoelectric materials is performed based on the non-local theory. After some manipulations, the impermeable crack, the permeable crack （the crack gap is full of NaCI solution）, and the semi-permeable crack （the crack gap is full of air or silicon oil） are reduced to a uniform formulation by assuming the normal electric displacement on the crack surfaces to be an unknown variable. Thus, a triple integral equation with the unknown normal electric displacement is established. By using the Newton iterative method and solving the triple integral equation, it is found that the normal electric displacement on the crack surfaces is no longer a constant as determined by previous studies, rather, it depends upon the remote combined electromechanical loadings. Numerical results of the stresses and electric displacement fields show that there are no singularities at the crack tips so that the stresses remain finite. It is of great significance that the concrete electric boundary condition on the crack surfaces exerts significant influence on the near-tip fields and in this way plays an important role in evaluating the crack stability in the non-local piezoelectric materials. More specifically, the impermeable crack model always overestimates the finite stresses at the crack tips, whereas the permeable crack model always underestimates them.     

Transient response of a central crack to a tensile pulse

This experimental investigation studies the opening displacement of a central electromachined slot in a thin aluminum plate subjected to an elastic tensile pulse. The tensile pulse was generated by an impact apparatus, and in-plane displacements were measured by interferometric technique. Comparison with existing analytical and finite-element solutions was good for short times.     

The torsional stability of a cylinder subject to finite perturbations

The problem of torsional stability of a circular cylinder made from a compressible nonlinearly elastic material is solved for finite perturbations. In contrast to the classical theory of bifurcation, an infinite sequence of steady states that bounds the domain of allowed initial perturbations is constructed. The applicability of the classical three-dimensional linear theory of stability is evaluated. Voronezh University, Russia. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 133–136, March, 2000.     

Thermal/mechanical interaction of subcritical crack growth in tensile specimen

The mutually interacting thermal/mechanical effects are accounted for by retaining the rate of change of volume with surface dV/dA, in the surface/volume energy density theory. An exchange between surface and volume energy would thus prevail in accordance with the rates at which the loads are transmitted throughout the system. Obtained are results for a center-cracked specimen subjected to monotonically rising tensile load at the rate of . Eight load steps are taken with an even increment increase of 69 MPa starting from 276 MPa. The temperature is found to oscillate about the ambient condition as the crack grew incrementally in a stable fashion. What differed considerably from the plasticity theory are the local stress and strain distribution and the crack growth characteristics. This is particularly pronounced in regions close to the crack tip where the local strain rates and strain rate history change from element to element, an affect that is not accounted for in plasticity.     

Optimal design of a beam subject to bending: a basic application

The minimisation of both the mass and deflection of a beam in bending is addressed in the paper. To solve the minimisation problem, a multi-objective approach is adopted by imposing the Fritz John conditions for Pareto-optimality. Constraints on the maximum stress and elastic stability (buckling) of the structure are taken into account. Additional constraints are set on the beam cross section dimensions. Three different cross sections of the beam are analysed and compared, namely the hollow square, the I-shaped and the hollow rectangular cross sections. The analytical expressions of the Pareto-optimal sets are derived. As expected, the I-shaped beam exhibits the best compromise in structural performance, which is related on the particular loading considered.