Damage parameter

It was found, [13], that the concept of the distributed damage, addressed by L.M. Kachanov [lA], allows us to account for this discrepancy Introducing the damage parameter Y varying from 1 (no damage) to 0 (total damage), the creep law can be presented, [15], as... 

At elevated temperature a joint action of thermo-chemical concrete degradation, V, accounting for high temperature related micro-cracking and dehydration, and external load-related cracking, d, is described by the total damage parameter, D, given by [7],... 

For concrete at high temperature the most important is the effect of cracking and dehydration process on the material properties, e.g. porosity n=f(Thydr)> intrinsic permeability k=/(T/,(/,/r. /7. T), and its deformations. Irreversible part of strains and so called thermal creep are expressed as functions of thermochemical damage parameter V, [8],... 

The macroscopic behavior of a saturated porous material undergoing a dissolution of its linear elastic solid matrix is therefore described by the classical Biot s theory, where the poroelastic properties now depend on the morphological parameter . Formally, plays the role of a damage parameter accounting for the dissolution. 

The increase of thus induces a macroscopic creep under constant stress. Assuming an instantaneous diffusion of the solute within the pore space, the mechanical affinity is Am —psij/el. The strain concentration effect at the crack tip then implies that the dissolution process concentrates at this place and is negligible elsewhere. The rate of crack radius increase a is derived from (22) and gives the evolution f(t) of the damage parameter ... 

Fig. 6 Damage parameters observed during shear loading.

To determine the IDEFs as functions of the damage parameters D D, micromechanical analysis of the damaged laminate has to be performed. 

Thus, the lamina macrostresses, Eq. (12), and macrostrains, Eq. (13), are determined as explicit functions of the damage parameters. Consequently, first partial derivatives of IDEFs,... 

Nordberg, G.F. Strangert, P. "Risk Estimation Models Derived from Metabolic and Damage Parameter Variation In a Population," 1982, to be published. 

Elastic parameters plastic parameters Damage parameters... 

A failure mode is identified when stress results in a failure. However, such failure may not result in an unacceptable level of performance. Therefore, once a failure mode has been identified, a damage parameter, which correlates in an empirical fashion with the expected failure mode, must be generated as well to complete Phase I testing. 

Following failure mode identification (le, the material suspected of significant aging, the stress implicated in its aging, and the appropriate damage parameter, which quantifies the expected failure), Phase II kinetic analysis for the predictions of lifetimes is conducted. The usual kind of kinetic analysis is one that uses Arrhenius principles, but other types of kinetics may be necessary depending on the empirical form of the data. 

Although void growth and possibly lap shear data have been identified as possible quantitative measurements of failure modes and could be used as damage parameters, additional work using Urethane C (see candidate identification) and/or one of the epoxies must be done to ensure the quantitative measurements are measuring only a single mode before Phase II kinetic analysis is begun. 

As far as the numerical implementation is concerned, it is required to (1) calculate the damage parameters at a given strain state, (2) redefine the elastic constants according to Eqn (2.1). An iteration procedure is needed to ensure convergence and... 

In the formula, K, D, e, P and a respectively are permeability coefficient of coal seam, permeability coefficient of raw coal, damage parameter of coal, increase multiples of permeability coefficient after damage, gas pressure coefficient of pore, coupling coefficient between the stress and the pore gas pressure. 

A damage parameter in damage mechanics (Kachanov 1980) is defined,... 

These results imply that the damage evolution and the accumulation of relative crack volume are also estimated from the moment tensor analysis. One example is given in Fig. 8.15. From moment tensors determined in bending tests of concrete specimens with a notch (Ohtsu and Ohtsuka 1998), the damage parameter and the accumulation of crack volume are estimated. In the case of the center-notched specimen (type CC), the damage suddenly increases, while the damage evolution is gradual in the off-center notched specimen (type OC). 

Thus far, the relationships apply to an isolated craze embedded in a specimen. To evaluate the energy release associated with an ensemble of crazes, the interaction of the crazes must be considered. In Reference 56, a damage parameter, similar in fashion to that introduced by Bristow (57), for a two-dimensional case was considered ... 

A local model of a solder joint can be found in Hg. 59.17. The local model is subjected to multiple thermal cycles and a final damage parameter is extracted. A typical thermal cycling loading profile to which the model is subjected is similar to that shown in Fig. 59.3. About two to four cycles are run to achieve stability of the hysteresis loop. 

Plastic work and plastic strain are two of the most common local damage parameters employed in solder joint lifetime estimations. The type of damage parameter selected is usually dictated by the experimental data available for a specific joint type (BGA, CCGA) that correlate damage with fatigue life. A methodology that employs plastic work and a correlation between plastic work and crack initiation and propagation can be found in References 10 and 46. 

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