On the Prediction of the Flow Behavior of Metals and Alloys at a Wide Range of Temperatures and Strain Rates Using Johnson–Cook and Modified Johnson–Cook-Based Models: A Review

Abstract

This paper reviews the flow behavior and mathematical modeling of various metals and alloys at a wide range of temperatures and strain rates. Furthermore, it discusses the effects of strain rate and temperature on flow behavior. Johnson–Cook is a strong phenomenological model that has been used extensively for predictions of the flow behaviors of metals and alloys. It has been implemented in finite element software packages to optimize strain, strain rate, and temperature as well as to simulate real behaviors in severe conditions. Thus, this work will discuss and critically review the well-proven Johnson–Cook and modified Johnson–Cook-based models. The latest model modifications, along with their strengths and limitations, are introduced and compared. The coupling effect between flow parameters is also presented and discussed. The various methods and techniques used for the determination of model constants are highlighted and discussed. Finally, future research directions for the mathematical modeling of flow behavior are provided.

Dynamic Mechanical Properties and Modified Johnson-Cook Model Considering Recrystallization Softening for Nickel-Based Powder Metallurgy Superalloys

“…According to Section 4.1.1, the FGH96 superalloy exhibits a strain rate strengthening effect in the plastic deformation stage. To describe the degree of strain rate strengthening of the material, the strain rate sensitivity coefficient q is introduced, as shown in Equation (14). The larger the strain rate sensitivity coefficient q, the stronger the strain rate sensitivity of the material.…”

“…As the most widely used phenomenological model, the Johnson-Cook (J-C) model [12] is given in the form of a three-part product, representing strain hardening, strain rate hardening, and thermal softening, respectively. However, the above three items of the J-C model are considered to be independent of each other, and the effects of the microstructure of the material itself and the adiabatic temperature rise on the flow stress are not considered [13][14][15].…”

INCONEL® Alloy Machining and Tool Wear Finite Element Analysis Assessment: An Extended Review

“…ε. Due to the inherent flaws of the JC model, as addressed in this section, some improvements have been developed, such as the derivations in [25][26][27]. The JC model is deemed a rate-independent constitutive model [28], along with the other models detailed in Table 1, and the expression for the stress in the JC constitutive model (σ JC ) is provided in Equation (1):…”

Modified Fields-Backofen and Zerilli-Armstrong constitutive models to predict the hot deformation behavior in titanium-based alloys

“…To predict the flow behavior, several constitutive models have been utilized which can be classified into three different categories namely phenomenological-based, physical-based, and artificial neural network models 16 , 17 . The phenomenological-based models mainly depend on empirical observations of stresses and strains such as Khan-Huang-Liang 18 , Johnson–Cook 19 and Fields-Backofen 20 models, while the physical-based models are mostly based on dislocation and dynamic softening phenomena during plastic deformation such as Zerilli-Armstrong 21 , Goetz-Seetharaman 22 and Preston-Tonks-Wallace 23 models, and the artificial neural network models uses artificial intelligence 24 – 27 .…”