Determination of the plasticity of metals by impact indentation of a spherical indenter

The problems of measuring the plastic characteristics of metals are considered. It is shown that the characteristics of materials used to compare their plasticity are not comparable and depend in the different degrees on the values of strain, strain rate, and modulus of elasticity. At the same time, the value of plasticity is more physically substantiated, which is determined by the ratio of plastic strain to total strain. It is shown that one of the optimal methods for measuring plasticity (plasticity index) is indentation. The possibility of using impact microindentation for this purpose is studied and expressions are proposed that allow calculating the plasticity based on the results of a single indentation of a spherical indenter. The specialties of the calculation of strain for this type of testing are shown. It was found that the values of plasticity obtained from the ratios of the depths of the plastic and elastic penetration of the indenter are equivalent to the values calculated from the energy ratios upon impact. Experimental studies have been carried out on metals with different hardness and type of crystal lattice. For the first time, the effect of strain rate, deformation, and impact energy (initial impact velocity) on the calculated value of plasticity when a sphere is impressed with strain rates of ~ 103 s–1 is shown. It is shown that when the strain corresponding to the onset of full plasticity during indentation is reached, the maximum sensitivity of the measured plasticity parameter for various metals is achieved.

Crack Tip Constraint for a Surface Crack Under Fully Plastic Conditions

The development of the crack shape in a thick wall pressure vessel is important in fitness-for-service evaluations such as leak-before-break. In this work the crack tip stress field for surface cracks in a thick plate is investigated using 3-D finite element analyses. The mean stress around the crack from the deepest point to the free surface is investigated for a semi-circular surface breaking crack. A new empirical procedure is developed that allows ductile crack growth to be modelled on the basis of standard deep and shallow cracked fracture toughness test data. In conjunction with this procedure the results show that the crack growth will be suppressed at the deepest segments and the crack will preferentially grow in direction of 45°–70° measured from the deepest point in full plasticity.

Two-Parameter Characterization of Elastic-Plastic Crack-Tip Fields

Plane-strain elastic-plastic crack-tip fields have been modeled with modified boundary layer formulations based on the first two terms K and T, of the elastic field. These formulations match the appropriate full field solutions. Compressive T stresses reduce the stresses by an amount which is independent of radial distance, corresponding to the introduction of a second term in addition to the dominant plastic singularity. Geometries which maintain J-dominance are characterized by zero or positive T stresses, while geometries with negative T stresses can be described by a two-parameter characterization using J and T into full plasticity.

Axisymmetric Elastic-Plastic Buckling of Axial and Pressure Loaded Cylinders

An analytical approach to the axisymmetric elastic buckling of isotropic cylinders, under arbitrary combinations of radial pressure and axial loading, is used as the basis of a first surface yield and a first full plasticity criterion of plastic collapse. Bending disturbances caused by the boundary constraint of both Poisson bulging under axial loading and the effects of arbitrary radial pressure loading are combined with any prescribed initial geometric errors to provide total ‘equivalent imperfection parameters’ on an otherwise perfectly cylindrical prebuckling state. Elasto-plastic collapse loads are then summarized in terms of just three parameters: the total equivalent membrane and bending imperfections parameters and the ratio of the minimum elastic classical critical axial stress to the material yield stress. The ease with which shells of arbitrary end conditions or internal ring stiffener supports can be treated, the consideration that the results so closely reproduce and extend the more elaborate numerical solutions, and the possible simplifications of the method, make it an ideal basis for design against axisymmetric collapse.