The Proceedings of the Eighth International Conference on Creationism (2018)

Our present study builds upon Sherburn et al. (2013) and includes additional rheological mechanisms that likely played important roles and also contributed to the rapid runaway process of the cataclysm. These additions include the following: 1) Pressure dependence on the yield strength (we model the yield strength using a yield surface concept that defines the boundary between elasticity and inelasticity in all directions), of the hardening, and of the recovery in the ISV equations. Also, the texture effect was included in the hardening to capture stress-state dependent mechanical behavior. 2) We added a recrystallization model to investigate its overall effects on the runaway process. 3) We added a grain size growth and reduction model that can track the grain size progression history. In this grain size model, the growth and reduction kinetics of olivine’s grains are simultaneously calculated based on actual laboratory data, and the average grain size is determined from a competition between the grain size growth and reduction. The resulting average grain size in turn influences the rock strength. What follows is a brief description of each of these additions to the overall ISV model. A. Isotropic and kinematic hardening equations of the ISV constitutive model Aprimary goal in the development of the ISVmodel was to capture the dislocation density changes that occur when a polycrystalline material is deformed. Toward that end, the ISV model attempts to represent as realistically as possible two main mechanisms related to the dislocation density change that simultaneously operate during the deformation: 1) hardening due to the dislocation density increase, and 2) weakening due to the dislocation density decrease. Work hardening occurs when the dislocations build up, while recovery occurs when the dislocations glide and annihilate on a slip plane (dynamic recovery) or climb on a slip plane that is perpendicular to the plane (static recovery). These two microstructural recovery mechanisms are essentially equivalent to the processes known within the geophysics community as dislocation creep and diffusion creep, respectively. In the ISV model, two crucial quantities are the isotropic (κ) and kinematic (ᾶ) hardening, which represent stress-like quantities arising from accumulations of statistically stored (isotropic) dislocations and geometrically necessary (anisotropic) dislocations during the deformation, respectively. Two hardening rate equations in the ISV model each include a hardening and two recovery terms as follows: (1) (2) where H is the isotropic work hardening, h is the kinematic work hardening, R d is the isotropic dynamic recovery, r d is the kinematic dynamic recovery, R s is the isotropic static recovery, r s is the kinematic static recovery, is the deviatoric inelastic strain rate, X is the recrystallized volume fraction, d 0 is the initial grain size, d is the current grain size, and z is the grain size-stress exponent. All the hardening and recovery terms are dependent on temperature and pressure. When the pressure increases, the total hardening rate increases; whereas when the temperature increases, the hardening rate decreases. As shown in both Eqs. (1) and (2), the recrystallization and the grain size effects are included. These equations show that increasing the volume fraction of recrystallized grains decreases the work hardening rate. Also, as the grain size increases, both work hardening and static recovery decrease by the same factor; therefore, competition between the two grain size effects are automatically incorporated. In summary, a reduction in hardening translates to a reduction in rock strength. B. Recrystallization Experimental studies on recrystallization, for both metals and rocks, find that the rate of recrystallized grain volume fraction change tends to obey the following relationship: (3) where X is the recrystallized grain volume fraction (Brown and Bammann 2012). When old grains recrystallize, previous dislocations are destroyed as new grains are formed. As mentioned in the preceding section, as the recrystallized volume fraction increases, the material strength decreases. Based on these ideas, we developed the following mathematical description of the recrystallization process: (4) (5) (6) (7) where Ẋ drx is the dynamically recrystallized volume fraction progression rate, Ẋ srx is the statically recrystallized volume fraction progression rate, μ is the shear modulus, X ∞ is the maximum volume fraction of recrystallization, c x 1 and c x 3 are the recrystallization rate constants of dynamic and static recrystallization, respectively, c x 2 and c x 4 are the temperature dependent constants, c dp and c sp are the pressure dependent constants, c xa and c xb are the sigmoidal shape constants, and c x 5 and c x 6 are the maximum recrystallized volume constants. C. Grain size kinetics Grain size kinetics can be divided into separate growth and reduction components. The model for grain growth kinetics is well established. Since this grain growth mechanism is driven by the thermodynamic energy, the following Arrhenius type equation is typically used: (8) where d is the grain size, n is the grain growth exponent, k 0 is the grain growth rate constant, is the activation energy for the grain growth, P is the pressure, is the activation volume for the grain growth, R is the gas constant, T is the temperature, a and b are the constants of volume fraction effect in a multi-mineral composition Cho et al. ◀ Strength-reducing mechanisms in mantle rock during the Flood ▶ 2018 ICC 711