Weibull modulus for diverse strength due to sample-specificity

By sample specificity it is meant that specimens with the same nominal material parameters and tested under the same environmental conditions may exhibit different behavior with diversified strength. Such an effect has been widely observed in the testing of material failure and is usually attributed to the heterogeneity of material at the mesoscopic level. The degree with which mesoscopic heterogeneity affects macroscopic failure is still not clear. Recently, the problem has been examined by making use of statistical ensemble evolution of dynamical system and the mesoscopic stress re-distribution model (SRD). Sample specificity was observed for non-global mean stress field models, such as the duster mean field model, stress concentration at tip of microdamage, etc. Certain heterogeneity of microdamage could be sensitive to particular SRD leading to domino type of coalescence. Such an effect could start from the microdamage heterogeneity and then be magnified to other scale levels. This trans-scale sensitivity is the origin of sample specificity. The sample specificity leads to a failure probability Phi (N) with a transitional region 0 < (N) < 1, so that globally stable and catastrophic modes could co-exist. It is found that the scatter in strength can fit the Weibull distribution very well. Hence, the Weibull modulus is indicative of sample specificity. Numerical results obtained from the SRD for different non-global mean stress fields show that Weibull modulus increases with increasing sample span and influence region of microdamage.

The investigation on dynamic fracture behavour of materials under compressive-shear combined stress waves

In this paper, an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials, under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond range. The impacting tests are carried out on the pressure-shear gas gun. The loading rate achieved is dK/dt similar to 10(8) MPa m(1/2) s(-1). With the elimination of influence of the specimen boundary, the plane strain state of a semi-infinite crack in an infinite elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the "momentum trap" technique. Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected from the specimen boundary or diffracted from the crack surfaces. In the current study, some important phenomena have been observed. The special loading of the single pulse can bring about material damage around crack tip, and affect the material behavior, such as kinking and branching of the crack propagation. Failure mode transitions from mode I to mode II crack are observed under asymmetrical impact conditions. The mechanisms of the dynamic crack propagation are consistent with the damage failure model.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic–plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a “hold” period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and “hold-at-the-maximum-indenter-displacement” for determining the instantaneous modulus using spherical indenters.

Size-Dependent Elastic Modulus And Fracture Toughness Of The Nanofilm With Surface Effects

The effective elastic modulus and fracture toughness of the nanofilm were derived with the surface relaxation and the surface energy taken into consideration by means of the interatomic potential of an ideal crystal. The size effects of the effective elastic modulus and fracture toughness were discussed when the thickness of the nanofilm was reduced. And the dependence of the size effects on the surface relaxation and surface energy was also analyzed.

An Improved Energy Method For Determining Young'S Modulus By Instrumented Indentation Using A Berkovich Tip

We previously proposed a method for estimating Young's modulus from instrumented nanoindentation data based on a model assuming that the indenter had a spherical-capped Berkovich geometry to take account of the bluntness effect. The method is now further improved by releasing the constraint on the tip shape, allowing it to have a much broader arbitrariness to range from a conical-tipped shape to a flat-ended shape, whereas the spherical-capped shape is just a special case in between. This method requires two parameters to specify a tip geometry, namely, a volume bluntness ratio V-r and a height bluntness ratio h(r). A set of functional relationships correlating nominal hardness/reduced elastic modulus ratio (H-n/E-r) and elastic work/total work ratio (W-e/W) were established based on dimensional analysis and finite element simulations, with each relationship specified by a set of V-r and h(r). Young's modulus of an indented material can be estimated from these relationships. The method was shown to be valid when applied to S45C carbon steel and 6061 aluminum alloy.

Experimental Verification And Theoretical Analysis Of The Relationships Between Hardness, Elastic Modulus, And The Work Of Indentation

The relationship between hardness (H), reduced modulus (E-r), unloading work (W-u), and total work (W-t) of indentation is examined in detail experimentally and theoretically. Experimental study verifies the approximate linear relationship. Theoretical analysis confirms it. Furthermore, the solutions to the conical indentation in elastic-perfectly plastic solid, including elastic work (W-e), H, W-t, and W-u are obtained using Johnson's expanding cavity model and Lame solution. Consequently, it is found that the W-e should be distinguished from W-u, rather than their equivalence as suggested in ISO14577, and (H/E-r)/(W-u/W-t) depends mainly on the conical angle, which are also verified with numerical simulations. (C) 2008 American Institute of Physics.

Nanoindentation of thin-film-substrate system: Determination of film hardness and Young's modulus

In the present paper, the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models. Aluminum film and two kinds of substrates; i.e. glass and silicon, are studied. Nanoindentation XP II and continuous stiffness mode are used during the experiments. In order to avoid the influence of the Oliver and Pharr method used in the experiments, the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption. The volume fraction model (CZ model) proposed by Fabes et al. (1992) is used and modified to analyze the measured hardness. The method proposed by Doerner and Nix (DN formula) (1986) is modified to analyze the measured Young's modulus. Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature, which include the results of two kinds of systems, i.e., a soft film on a hard substrate and a hard film on a soft substrate. In the modified CZ model, the indentation influence angle, phi, is considered as a relevant physical parameter, which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.

Effective elastic modulus of bone-like hierarchical materials

A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis.

Effect of a laser pre-quenched steel substrate surface on the crack driving force in a coating-steel substrate system

A mechanical model of a coating/laser pre-quenched steel substrate specimen with a crack oriented perpendicular to the interface between the coating and the hardened layer is developed to quantify the effects of the residual stress and hardness gradient on the crack driving force in terms of the J-integral. It is assumed that the crack tip is in the middle of the hardened layer of the pre-quenched steel substrate. Using a composite double cantilever beam model, analytical solutions can be derived, and these can be used to quantify the effects of the residual stress and the hardness gradient resulting from the pre-quenched steel substrate surface on the crack driving force. A numerical example is presented to investigate how the residual compressive stress, the coefficient linking microhardness and yield strength and the Young's modulus ratio of the hardened layer to the coating influence the crack driving force for a given crack length. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Simple phenomenological determination of contact stiffness and elastic modulus of Ce-based bulk metallic glasses through nanoindentation

The viscoelastic deformation of Ce-based bulk metallic glasses (BMGs) with low glass transition temperature is investigated at room temperature. Contact stiffness and elastic modulus of Ce-based BMGs cannot be derived using the conventional Oliver-Pharr method [W. C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564 (1992)]. The present work shows that the time dependent displacement of unloading segments can be described well by a generalized Kelvin model. Thus, a modified Oliver-Pharr method is proposed to evaluate the contact stiffness and elastic modulus, which does, in fact, reproduce the values obtained via uniaxial compression tests. (c) 2007 American Institute of Physics.