# Virtual Sensor for Estimating the Strain-Hardening Rate of
###### Abstract
However, this process is both costly and time-consuming, estimated at 49 man hours per sheet of each ASS, and also requests physical samples, the availability of which can be limited, especially for newly designed materials or those under development. Then, the use of regression models is proposed as an economical and faster way of conducting such studies [30]. More recently, the concept of virtual sensors has been introduced in the industrial sector as a potential solution to reduce the risk of high-impact failures by improving detectability and predicting failure modes [31]. Examples of this technological advancement are the works of [PERSON] et al. [32], who developed a virtual sensor to replace a semi-manual procedure of the verification of the final chemical composition of stainless steels, and [PERSON] et al. [33], who designed a model for geometry prediction after cold strain based on the virtual sensor for robotic sheet metal forming. Stainless steel sheets are commonly subjected to forming processes to achieve the final product shape. During these processes, the steel undergoes cold strain hardening. The strain state and the strain-hardening rate are critical factors that influence the success of the sheet deformation process. Thus, from a manufacturing standpoint, it is very beneficial to develop a mathematical model to estimate the strain-hardening rate across a broad spectrum of ASS. Such a model would enable the prediction of the material behaviour prior to forming, thereby facilitating an assessment of its cold workability. This paper aims to develop a new parameter for estimating the strain-hardening rate of traditional and new-generation ASS, which are used for applications such as in the food industry, drawing, furnaces, or decoration elements, among others. This development is based on the results obtained from a multiple linear regression (MLR) analysis, correlating \(Rm\) with chemical composition and thickness reduction [29]. To accomplish this, a wide selection of ASS underwent cold rolling at the laboratory scale, encompassing various thickness reductions, followed by uniaxial tensile testing to obtain experimental cold-rolling curves. A database is compiled from these curves, facilitating the establishment of a linear regression (LR) model that expresses \(Rm\) as a function of the cold thickness reduction for each austenitic grade. Subsequently, based on the Hollomon procedure which defines the strain-hardening exponent \(n\) as the slope of the linear relation between the logarithm of stress and the logarithm of strain, and referencing the work of [PERSON] et al. [16] for low carbon steel, the slope of each linear relation between \(Rm\) and the cold thickness reduction is determined and defined as the strain-hardening rate of each ASS grade. Finally, these slopes are denoted as coefficient \(a\) and correlated with the chemical composition through MLR, culminating in the formulation of the new strain-hardening rate parameter designated as \(HRHS\) (_Hardening Rate of Hot rolled and annealed Stainless steel sheet_). Thisparameter can serve as a virtual sensor for the design and development of new ASS grades, as well as for optimizing cold-forming processes.