Indentation of a hard sphere into inelastic solids, Brinell indentation, is examined theoretically and numerically by aid of classical plastic flow theory. With the main interest focused on fully plastic behaviour at indentation the mechanical analysis is carried out for power-law hardening rigid-plastic materials where self-similarity features play a dominant role. It is explained in detail how the problem of a moving contact boundary may be reduced to a stationary one by an appropriate transformation of field variables. Within this setting classical empirical findings by Meyer (1908) and O'Neill (1944) are established on a rigorous theoretical ground. In particular, it is shown to advantage also for nonlinear materials how intermediate solutions for a flat die may by cumulative superposition generate solutions for a class of curved indenters. In the case of perfect plasticity it turns out in the present context that indentation hardness is independent of die profiles. For hardening solids when the material behaviour is history dependent, reduction to a stationary geometry is achieved also by expressing the accumulated strain by cumulative superposition. The intermediate flat die problem is then solved for a variety of hardening exponents by a finite element procedure designed to account for material incompressibility. With finite element computations as a basis desired solutions are obtained by straightforward numerical superposition procedures. Detailed results are then given for bulk quantities such as the mean contact pressure as well as relevant field variables. The influence of hardening characteristics on sinking-in and piling-up of indented surfaces and contact pressure distributions are discussed in the light of earlier findings based on deformation theory of plasticity and available discriminating experiments. Correlation is particularly sought with the celebrated universal hardness parameters proposed by Tabor (1951) and the existence of representative strain measures. Attention is also given to the elastic-plastic transition region of Brinell indentation in search for loading levels sufficiently high that the results tend to an asymptotic fully plastic state. A standard finite element technique employing contact elements for a moving boundary is used to analyse with tolerable accuracy the influence of elasticity and more elaborate hardening behaviour. Some relevant features are shown for a sequence of solutions from elastic Hertzian to fully plastic behaviour.

An analysis of fully plastic Brinell indentation

In order to test the accuracy of theoretical fracture models for mortar and concrete, it is necessary to have accurate measurements of the crack profiles. In this study, sandwich holographic interferometry has been used to find the crack profiles in a center-notched plate specimen loaded at the center of the notch. The results have shown that at low load levels with corresponding short crack lengths, there is little difference between the measured crack profiles and elastic crack profiles computed by finite-element analysis. At high loads with long crack lengths there is a large difference between measured and computed elastic crack profiles. The data suggest the presence of a closing pressure at the crack tip and that there may be a limit to crack-tip-opening displacement (CTOD) before the crack propagates.

Crack profiles in mortar measured by holographic interferometry

Micromechanisms of matrix fracture in Portland cement-based fiber composites were studied by means of reflection holographic interferometry and quantitative image analysis. An experimental investigation was conducted with different volume concentrations of polypropylene fibers. Uniaxial tensile specimens were loaded within a strain range of up to three percent. The deformation history was recorded as interference holograms. The holograms were acquired in an image-analysis system. After enhancement, they were analyzed for crack density, length, opening profile, and spacing. The evolution of microcracks, their propagation, distributed microcracking and the material response beyond the characteristic damage state are also discussed.

A study of fracture in fiber-reinforced cement-based composites using laser holographic interferometry

Derivation of tensile flow properties of thin films using nanoindentation technique

Local contact behavior between elastic and elastic–plastic bodies

Ball-indentation experiment ware performed with A723 steel of 100- to 1200-MPa ultimate strength. Results are compared with conventional tension tests and with an elastic-plastic finite-element model of the ball indentation. Finite-element analysis shows the ball-indentation process to be insensitive to friction effects. Comparison of indentation and conventional tests shows that slip-line field analysis closely predicts the ball contact stress. The indentation tests gave an accurate measure of ultimate tensile strength because of the following test procedures: using a large ball size and a fixed ratio of indentation depth to ball size; accounting for directional material properties; accounting for extraneous system deflections.

Analysis of Elastic-Plastic Ball Indentation to Measure Strength of High Strength Steels

An analysis is described of a welded stainless steel box beam that experienced a structural failure during fatigue testing. Cracks initiated at notches caused by partial penetration welds and grew to a length of several centimetres in about 1000 load cycles. The objective here is to describe the characterization of fracture toughness and fatigue crack initiation for the precipitation-hardening stainless steels used for the welds and parent plate of the beam. Three-point bend specimens were used to measure both fatigue crack initiation life and the J-integral fracture toughness of the parent plate and weld metal in various conditions. The notch fatigue analysis method of Barsom and Rolfe was used to analyze the crack initiation test results. The crack was grown further, side notches were added, and J 1 c tests were performed using ASTM Test Method for J 1 c , a Measure of Fracture Toughness (E 813-87) with a modified load-line-displacement unloading-compliance procedure to measure crack growth. Conclusions drawn from the work include the following: (a) J 1 c can be accurately determined with a three-point bend test using load-line displacement to measure crack growth by unloading compliance (An accurate expression for a/W in terms of load-line displacement was developed.); and (b) fatigue crack initiation life and J 1 c fracture toughness of stainless steels in various conditions were characterized. The welded and aged condition, with no intermediate solution treatment, showed unstable, cleavage-type fracture and resulted in a low J 1 c value and a short initiation life.

J. J. Zalinka

Papers

Analysis of Elastic-Plastic Ball Indentation to Measure Strength of High Strength Steels

Fracture Toughness and Fatigue Crack Initiation Tests of Welded Precipitation-Hardening Stainless Steel