PSI - Issue 13

Evgeny V. Shilko et al. / Procedia Structural Integrity 13 (2018) 1508–1513 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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where  is the strength ratio of “dry” ma terial under uniaxial compression (  uct ) and tension (  utt ), b is the dimensionless material coefficient,  eq is equivalent stress in the volume of discrete element. In the study we used  =3. This value is typical for brittle materials that do not contain large scale discontinuities. One can see that pore pressure has positive contribution to the criterion (2), namely increase in the value of P pore leads to onset of local fracture at smaller absolute values of mean and shear stresses in the skeleton. We modelled uniaxial compression of the model samples at a constant velocity V . Interstitial fluid was able to flow out of the deformed sample through the free side surfaces. In the study, we varied the axial strain rate V H    (within six orders of magnitude), the initial permeability of the material k 0 (within four orders of magnitude), the dynamic fluid viscosity  and sample radius R (both within an order of magnitude). The results of the study showed that the value of uniaxial compressive strength of fluid-saturated samples  c is determined by the balance of the contributions of two competing processes: 1) applied deformation, which provides compression of the pore volume and an increase in the pore fluid pressure; 2) the outflow of the compressed pore fluid through the side faces, which leads to a decrease in the pore pressure. Since the fluid flow rate is proportional to the gradient of the pore pressure, the increase in the strain rate (and consequently, the rates of compression of the fluid saturated micropores and pore pressure grow) is accompanied by an increase in the rate of fluid flow from the sample (i.e., in the rate of decrease in the pore pressure and its contribution to stress state and strength of the skeleton). At the same time, the absolute value of the flow rate is limited by the material parameters including viscosity of the fluid  and the permeability of the solid-phase skeleton of sample k . Therefore, an increase in the strain rate is accompanied by an increase in the value of P pore (at the same value of applied strain) and, consequently, by the onset of failure at lower value of applied axial stress. This corresponds to a decrease in the dynamic compressive strength of the sample. Fig. 1a shows strain rate dependence of the compressive strength  c of the model 3D sample with “basic” mechanical characteristics. 3. Results and discussion

Fig. 1. The dependences of the dynamic strength of the samples of fluid-saturated brittle material on strain rate (a) and dimensionless parameter R n (b). Points denote numerically derived values of strength at different strain rates, permeability values, sample radii and fluid viscosities. Black dashed line in (b) is an approximation of the set of points by sigmoid function (5). One can see that at low strain rates the magnitude of shear strength tends toward the upper limit (strength of “dry” material  uct ), and at high strain rates – toward the minimal value. This dependence is nonlinear (logistic-like) and is characterized by three regions. In region I (small loading rates), the rate of fluid outflow from the sample is sufficiently large to provide the drop in pore pressure to the atmospheric value. The influence of an interstitial fluid on the stress state of the samples is negligible, and their strength tends to the strength of a "dry" sample. In region III (high loading rates), the outflow of fluid from the sample does not compensate for the increase in fluid density during the deformation of the pores. Hence, during the course of deformation of the sample, the pore pressure constantly increases, which leads to a decrease in the dynamic strength of the sample. In the transition region II, the rate of decrease in the fluid density due to its outflow from the sample is comparable with the rate of increase in