PSI - Issue 10

V.N. Kytopoulos et al. / Procedia Structural Integrity 10 (2018) 272–279

273

V.N. Kytopoulos et al. / Structural Integrity Procedia 00 (2018) 000 – 000

2

discontinuities may appear in highly stressed parts. Such deterioration weakens the material and lowers its load carrying capacity. Due to their nature these defects are discrete entities. An accurate analysis of their influence would be to consider them as discrete disturbances of the material continuum, a prohibitive task (Budiansky and O’Connell (1976); Basaran and Nie (2004); Gyarmati (1970); Kestin and Rice (1970); Krajcinovic (1985); Krajcinovic et al. (1987); Lemaitre (1996); Hult (1975); Yang et al. (2005); Lemaitre and Desmorat (2005)). The continuity, ψ, introduced into the continuum damage mechanics, may be said to quantify the absence of ma terial deterioration. The complementary quantity D =1- ψ is therefore a measure of the state of micro-structural disinte gration or damage. For a completely undamaged material D =0, whereas D =1 corresponds to the state of complete loss of integrity of the material structure. Detailed knowledge about the conditions for deterioration of the material structure would make it possible to predict the load carrying capacity or lifetime without first performing extensive testing. However, up to now a detailed knowledge about these conditions could not be obtained. Nevertheless, now adays there exist a lot of experimental techniques applied to obtain detailed and valuable information in this direction (Krajcinovic et al. (1987); Lemaitre (1996); Lemaitre and Desmorat (2005); and Noukou (2006)). These techniques are based on microscopic and macroscopic damage measures to define and quantify materials damaging behavior. However, most of these techniques are cumbersome and labor time consuming; yet these techniques focus primarily on macroscopic response and damage quantification and secondarily on damage characterization based on internal mechanical macroresponse of material. Consequently, it would be of appreciable importance to establish in this direction certain practical and as possible as simple approaches to a more extensive characterization of damage behavior of materials. In this aspect, these approaches should be described by suitable operational parameters, by which the general trend of related damage-depended changes can more easily be followed, analyzed and better com pared to each other. In this study an attempt is made to establish appropriate semi quantitative approaches, which could be helpful for the above mentioned scopes. The evolution of the damage parameter depends on the development of the size of the flows and their number, which in turn is determined by microphysical process specific to the material under consideration. Elastic-brittle damage should apply to process with the duration of the strain pulse and the corresponding duration of the damage increment shorter by orders of magnitude than the relaxation time of rheological phenomena in the material. In this context, the elastic-brittle damage mechanics principles could be applied, in an approximating manner to moderate strain rates corresponding to low dynamic effects (Krajcinovic et al. (1987); Lemaitre (1996); Hult (1975); Yang et al. (2005); Lemaitre and Desmorat (2005)). It is postulated that in view of the accumulative property of damage an arbitrary process begins at some positive initial damage D 0 >0 at zero strain which means that brittle damage can develop only in elastic materials with imperfec tions. This means that a perfect damage-free material, if it could exist, should not be able to develop any damage. One of the basic problems of continuum damage theory is to find relationships between the two primary parameters, initial damage, D 0 and damage at failure, D f . Such a relationship is given as (Krajcinovic et al. (1987); Lemaitre (1996)):      f f f D D D D D 1 1 0 0 ln 1 (1) which determines damage at failure as a function of two parameters, namely the initial damage and power K. One finds that as initial damage tends to zero the damage at failure tends to the ultimate value of damage D=1. One also finds that with increasing initial damage there is a monotonic decrease in the value of failure damage for all admissible powers K, until the two damage variables meet at upper bound of the initial damage. Thus, such upper bound can be calculated to be D =0.49 (Krajcinovic et al. (1987); Lemaitre (1996)). Another basic primary parameter of damage mechanics is the dimensionless strain energy at failure ω f which can be calculated by a simplified equation: 2. Theoretical considerations

  

 D D D 1 1 0 1 f



 f

(2)

f