Relationships Between Initial Unloading Slope, Contact Depth, and Mechanical Properties for Conical Indentation in Linear Viscoelastic Solids

Using analytical and finite element modeling, we examine the relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in viscoelastic solids with either displacement or load as the independent variable. We then investigate whether the Oliver-Pharr method for determining the contact depth and contact radius, originally proposed for indentation in elastic and elastic-plastic solids, is applicable to spherical indentation in viscoelastic solids. Finally, the analytical and numerical results are used to answer questions raised in recent literature about measuring viscoelastic properties from instrumented spherical indentation experiments.

Theory Of Phase Transformation And Reorientation In Single Crystalline Shape Memory Alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

An anisotropic elastic-plastic constitutive model for single and polycrystalline metals. II—Experiments and predictions concerning thin-walled tubular OFHC copper

Predictions based on an anisotropic elastic-plastic constitutive model proposed in the first part of this paper are compared with the experimental stress and strain data on OHFC copper under first torsion to about 13% and partial unloading, and then tension-torsion to about 10% along eight different loading paths. This paper also describes the deformation and stress of the thin-walled tubular specimen under finite deformation, the numerical implementation of the model, and the detailed procedure for determining the material parameters in the model. Finally, the model is extended to a general representation of the multiple directors, and the elastic-viscoplastic extension of the constitutive model is considered.

A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading

In this paper, we attempted to construct a constitutive model to deal with the phenomenon of cavitation and cavity growth in a rubber-like material subjected to an arbitrary tri-axial loading. To this end, we considered a spherical elementary representative volume in a general Rivlin's incompressible material containing a central spherical cavity. The kinematics proposed by [Hou, H.S., Abeyaratne, R., 1992. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571-722] was adopted in order to construct an approximate but optimal field. In order to establish a suitable constitutive law for this class of materials, we utilized the homogenisation technique that permits us to calculate the average strain energy density of the volume. The cavity growth was considered through a physically realistic failure criterion. Combination of the constitutive law and the failure criterion enables us to describe correctly the global behaviour and the damage evolution of the material under tri-axial loading. It was shown that the present models can efficiently reproduce different stress states, varying from uniaxial to tri-axial tensions, observed in experimentations. Comparison between predicted results and experimental data proves that the proposed model is accurate and physically reasonable. Another advantage is that the proposed model does not need special identification work, the initial Rivlin's law for the corresponding incompressible material is sufficient to form the new law for the compressible material resulted from cavitation procedure. (C) 2007 Elsevier Ltd. All rights reserved.

Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading

The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snap-through occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.

Statistical formulation and experimental determination of growth rate of micrometre cracks under impact loading

A new statistical formulation and a relevant experimental approach to determine the growth rate of microcracks were proposed. The method consists of experimental measurements and a statistical analysis' on the basis of the conservation law of number density of microcracks in phase space. As a practical example of the method, the growth rate of microcracks appearing in an aluminium alloy subjected to planar impact loading was determined to be ca. 10 mu m/mu s under a tensile stress of 1470 MPa and load duration between 0.26 mu s and 0.80 mu s.

Elimination of loading reverberation in the split hopkinson torsional bar

The loading reverberation is a multiple wave effect on the specimen in the split Hopkinson torsional bar (SHTB). Its existence intensively destroys the microstructure pattern in the tested material and therefore, interferes with the study correlating the deformed microstructure to the macroscopic stress-strain response. This paper discusses the problem of the loading reverberation and its effects on the post-mortem observations in the SHTB experiment. The cause of the loading reverberation is illustrated by a stress wave analysis. The modification of the standard SHTB is introduced, which involves attaching two unloading bars at the two ends of the original main bar system and adopting a new loading head and a couple of specially designed clutches. The clutches are placed between the main bar system and the unloading bars in order to lead the secondary loading wave out of the main bar system and to cut off the connection in a timely manner. The loading head of the standard torsional bar was redesigned by using a tube-type loading device associated with a ratchet system to ensure the exclusion of the reflected wave. Thus, the secondary loading waves were wholly trapped in the two unloading bars. The wave recording results and the contrasting experiments for examining the post-mortem microstructure during shear banding both before and after the modification highly support the effectiveness of the modified version. The modified SHTB realizes a single wave pulse loading process and will become a useful tool for investigating the relation between the deformed microstructure and the macroscopic stress-strain response. It will play an important role especially in the study of the evolution of the microstructure during the shear banding process. (C) 1995 American Institute of Physics.

Inhomogeneous behavior of antiplane shear crack in softening material with local unloading

Examined in this work is the anti-plane stress and strain near a crack in a material that softens beyond the elastic peak and unloads on a linear path through the initial state. The discontinuity in the constitutive relation is carried into the analysis such that one portion of the local solution is elliptic in character and the other hyperbolic. Material elements in one region may cross over to another as the loading is increased. Local unloading can thus prevail. Presented are the inhomogeneous character of the asymptotic stress and strain in the elliptic and hyperbolic region, in addition to the region in which the material elements had experienced unloading. No one single stress or strain coefficient would be adequate for describing crack instability.

Fracture behavior of axisymmetrical bars under high triaxial stress and large strain cyclic loading

Axisymmetric notched bars with notch roots of large and small radii were tested under large strain cyclic loading. The main attention is focused on the fracture behaviour of steels having cycles to failure within the range 1-100. Our study shows that a gradual transition from a static ductile nature to one of fatigue cleavage can be observed and characterized by the Coffin-Manson formula in a generalized form. Both the triaxial tensile stress within the central region of specimens and static damage caused by the first increasing load have effects on the final failure event. A generalized cyclic strain range parameter DELTAepsilon is proposed as a measure of the numerous factors affecting behaviour. Fractographs are presented to illustrate the behaviour reported in the paper.

On dilatational plastic constitutive equation of ductile materials and plastic loading paths at bifurcation

The dilatational plastic constitutive equation presented in this paper is proved to be in a form of generality. Based on this equation, the constitutive behaviour of materials at the moment of bifurcation is demonstrated to follow a loading path with the response as "soft" as possible.