# Virtual Sensor for Estimating the Strain-Hardening Rate of
###### Abstract
Mechanical testing is commonly used to quantitatively analyse the combined effect of all these different hardening mechanisms. The two most widely used tools are the strain-hardening exponent \(n\), determined from the engineering stress-strain flow curve obtained from tensile tests [15], and the cold-rolling curves, which plot the evolution of the mechanical properties against the thickness reduction [16,17]. During the last decade, multiple works have been published, supporting the modelling of these mechanical parameters for several traditional ASS. One of the most extensively modelled aspects is the cold-strain-hardening behaviour of the AISI 304 austenitic. Several studies have reported nonlinear stress-strain models under various testing conditions; [PERSON] et al. [15] proposed a revised predictive equation for the strain-hardening parameter \(n\) for the AISI 304 based on the [PERSON] model, while [PERSON] et al. [18] designed a new stress-strain model to accurately predict both tensile and compressive full-range stress-strain curves for the AISI 304. Furthermore, [PERSON] et al. [19] established eight constitutive relations to predict the flow stress curves of the AISI 304 under different conditions of strain-hardening rate and temperature. In addition to these studies, [PERSON] et al. [20] modelled the relationship between cold deformation and the mechanical properties of austenitic AISI 316L, combining theoretical analysis, numerical simulation and experimental uniaxial tensile testing. Moreover, [PERSON] et al. [21] established a linear correlation between austenite deformation and martensite transformation for low-Ni ASS. The model predicts the stress-strain curve from the parameter \(M_{s}\); this describes the initial temperature of the martensitic transformation and is related to the austenite stability. The majority of these studies demonstrate the distinct stages of strain-hardening behaviour in ASS, as evidenced by the stress-strain curves. The plastic deformation in these steels is greatly influenced by the microstructural phase transformation, which is the primary challenge in accurately modelling strain-hardening behaviour. Consequently, developing a single model to describe strain-hardening behaviour across a wide range of ASS becomes extremely difficult [22]. To address the complexity of simulating the strain-hardening behaviour of ASS, cold-rolling curves offer an accepted solution for estimating the strain-hardening rate by correlating the tensile strength (\(Rm\)) of steel with different cold-rolling deformations and the cold thickness reductions applied. This approach, as proposed by [PERSON] et al. for low-carbon steel [16], involves fitting the relationship between Rm with several cold-rolling and respective deformations to a second-degree polynomial equation, and then, using the Hollomon procedure to determine the strain-hardening exponent \(n\). This is achieved by determining the slope of the linear relation between the logarithm of \(Rm\) and the logarithm of cold thickness reduction for the cold-rolled low-carbon steel. In the field of ASS, several authors have reported experimental cold-rolling curves such as AISI 304 [23], 304L [24], 316 [25], and 201 [26; 27] showing different evolutions of the mechanical properties and microstructure against the cold thickness reduction, depending on the steel grade. Various works have confirmed the effect of the chemical composition on mechanical behaviour. [PERSON] et al. [14] confirmed the classical relationship of the \(Rm\) and \(Rp_{0.2}\) with the solute concentration for the AISI 304 proposed by [PERSON] et al. [28], and [PERSON] et al. [29] demonstrated a linear relationship of the mechanical properties with the chemical composition and the cold thickness reduction for stainless steels. Therefore, determining the strain-hardening rate of a specific ASS requires experimental analysis.