From 4ca79367037f3290a9c99c15b8574b76b4919af6 Mon Sep 17 00:00:00 2001 From: David Torres Date: Fri, 15 Nov 2024 11:18:22 -0500 Subject: [PATCH] fixes to JC documentation #000 --- .../hardening_models/JohnsonCookHardening.md | 14 +++++++------- doc/content/theory/constitutive_models.md | 1 + 2 files changed, 8 insertions(+), 7 deletions(-) diff --git a/doc/content/source/materials/hardening_models/JohnsonCookHardening.md b/doc/content/source/materials/hardening_models/JohnsonCookHardening.md index c64fd23bb68..b789ed56ccf 100644 --- a/doc/content/source/materials/hardening_models/JohnsonCookHardening.md +++ b/doc/content/source/materials/hardening_models/JohnsonCookHardening.md @@ -6,25 +6,25 @@ The Johnson-Cook plasticity model has the following form \begin{equation} - \sigma = \sigma_0\left(A+B\left(\frac{\ep}{\ep0}\right)^n\right)\left(1+C\text{ln}\left(\frac{\epdot}{\epdot0}\right)\right)\left(1-\left(\frac{T-T_0}{T_m-T_0}\right)^m\right) + \sigma = \sigma_0\left(A+B\left(\frac{\ep}{\varepsilon_0^p}\right)^n\right)\left(1+C\text{ln}\left(\frac{\epdot}{\dot\varepsilon_0^p}\right)\right)\left(1-\left(\frac{T-T_0}{T_m-T_0}\right)^m\right) \end{equation} -Where $\sigma_0$ is the unperturbed yield stress, $\ep0$ is the reference plastic strain, $\epdot0$ is the reference plastic strain rate, $T_m$ is the melting temperature, and $T_0$ is the reference temperature. +Where $\sigma_0$ is the unperturbed yield stress, $\varepsilon_0^p$ is the reference plastic strain, $\dot\varepsilon_0^p$ is the reference plastic strain rate, $T_m$ is the melting temperature, and $T_0$ is the reference temperature. $A$,$B$,and $C$ are parameters of the Johnson-Cook model. When put into a variational framework, the Johnson-Cook model defines the following plastic energy \begin{equation} -\psi_p = \left[\left(1-Q\right)g_p \sigma_0 \ep \left(A\ep + B\ep0\left(\frac{\ep}{\ep0}\right)^{n+1}\frac{1}{n+1}\right)\right]f(T),\\ -\psi_p^* = \left[Q \sigma_0\left(A+B\ep0\left(\frac{\ep}{\ep0}\right)^n\right)+\left(A+B\frac{\ep}{\ep0}\right)\left(C\text{ln}\left(\frac{\epdot}{\epdot0}\right)-C\right)\right]f(T),\\ -f(T) = \left(\frac{T-T_0}{T_m-T_00}\right) +\psi_p = \left[\left(1-Q\right)g_p \sigma_0 \ep \left(A\ep + B\varepsilon_0^p\left(\frac{\ep}{\varepsilon_0^p}\right)^{n+1}\frac{1}{n+1}\right)\right]f(T),\\ +\psi_p^* = \left[Q \sigma_0\left(A+B\varepsilon_0^p\left(\frac{\ep}{\varepsilon_0^p}\right)^n\right)+\left(A+B{\left(\frac{\ep}{\varepsilon_0^p}\right)^n}\right)\left(C\text{ln}\left(\frac{\epdot}{\dot\varepsilon_0^p}\right)-C\right)\right]f(T),\\ +f(T) = \left(\frac{T-T_0}{T_m-T_0}\right) \end{equation} Additionally, the energy is split into energetic and dissipative portions using the Taylor-Quinney factor, $Q$.\\ The flow stresses are defined as the following \begin{equation} - Y^{\text{eq}}=\left[\left(1-Q\right)\sigma_0\left(A+B\frac{\ep}{\ep0}\right)^n\right]f(T),\\ - Y^{\text{vis}}=\left[Q\sigma_0\left(A+B\left(\frac{\ep}{\ep0}\right)^n\right)+\left(A+B\frac{\ep}{\ep0}\right)\left(C\text{ln}\left(\frac{\epdot}{\epdot0}\right)\right)\right]f(T) + Y^{\text{eq}}=\left[\left(1-Q\right)\sigma_0\left(A+B\frac{\ep}{\varepsilon_0^p}\right)^n\right]f(T),\\ + Y^{\text{vis}}=\left[Q\sigma_0\left(A+B\left(\frac{\ep}{\varepsilon_0^p}\right)^n\right)+\left(A+B\frac{\ep}{\varepsilon_0^p}\right)\left(C\text{ln}\left(\frac{\epdot}{\dot\varepsilon_0^p}\right)\right)\right]f(T) \end{equation} diff --git a/doc/content/theory/constitutive_models.md b/doc/content/theory/constitutive_models.md index fccc7794670..e0b40b9b87d 100644 --- a/doc/content/theory/constitutive_models.md +++ b/doc/content/theory/constitutive_models.md @@ -33,6 +33,7 @@ We support both small deformation and large deformation. Several hyperelastic mo - [Power-law hardening](PowerLawHardening.md) - [Arrhenius-law hardening](ArrheniusLawHardening.md) +- [Johnson-Cook Hardening](JohnsonCookHardening.md) ## Phase-field fracture models