Sensitivity analysis of temperature in heated soft tissues with respect to time delays

Axisymmetric tissue region heated by an external heat flux is considered. The mathematical model is based on the dual-phase lag equation supplemented by appropriate boundary and initial conditions. This equation, in relation to the Pennes’ equation, has two additional parameters, namely the relaxation time and the thermalization time. The aim of this research is to estimate the temperature changes due to changes of these parameters. To achieve this, sensitivity analysis methods are used. The basic problem and additional ones related to the sensitivity functions are solved using the implicit scheme of the finite difference method. The performed computations show that the temperature changes caused by changes in the relaxation and thermalization times are larger for higher values of the external heat flux and shorter times of its action.

An implicit integration scheme with consistent tangent modulus for Leblond’s model of transformation-induced plasticity in steels

Thermomechanical treatments involving solid-state phase transformations play an important role for the manufacturing of functional and reliable components in many engineering applications. Accordingly, numerical investigation and optimization of such processes require considering thermoelastoplasticity under the influence of ongoing transformations and in particular the impact of transformation-induced plasticity (TRIP). While a number of elaborate plasticity models have been proposed for the description of TRIP, none of them seem to have received much prevalence in applications due to their complexity or hard to determine model parameters. Instead, the overwhelming majority of applied research either relies on simplistic formulations dating back to early phenomenological approaches or neglects TRIP altogether. In this work, we therefore provide an accessible, straightforward and easy-to-implement solution scheme for the TRIP model proposed by Leblond et al. which, despite being widely recognized, is hardly ever employed in full form. Specifically, we employ implicit backward-Euler integration and an elastic–plastic operator split approach to update the stresses in order to obtain a simple and concise algorithm for which we then derive the corresponding consistent tangent modulus. Furthermore, the work contains an application of the solution scheme to a symmetrically cooled plate and an in-depth discussion of the influence of TRIP by means of this tractable numerical example. Specifically, we highlight the discrepancies arising in transient and residual stresses and strains compared to the conventional $$J_2$$ J 2 -plasticity approach where the phase transformation is accounted for merely by adapting the yield strength of the compound.

Strain-hardening properties of the high-entropy alloy MoNbTaTiVZr processed by high-pressure torsion

An equiatomic MoNbTaTiVZr refractory high-entropy alloy (HEA) produced by arc melting was processed by high-pressure torsion (HPT) at room temperature. Thermodynamic calculations and experimental results indicated a dual-phase microstructure composed of about 85% BCC Zr-depleted and 15% BCC Zr-rich phase in the as-cast condition. HPT causes grain refinement and an increase in dislocation density without the formation of new phases. After four revolutions, the Zr-depleted phase was hardened to $$\sim $$ ∼ 540 HV, while the Zr-rich phase exhibited softening with a decrease in hardness to $$\sim $$ ∼ 480 HV. The occurrence of a vortex-like microstructure and the analysis of elemental concentrations indicated a shear-induced mechanical homogenization, which was supposed to be the cause of the observed softening.