Name: TIAGO BRISTT GONORING
Publication date: 03/04/2023
Advisor:
Name |
Role |
|---|---|
| MARCOS TADEU DAZEREDO ORLANDO | Advisor * |
Examining board:
| Name |
Role |
|---|---|
| CARLOS AUGUSTO CARDOSO PASSOS | Internal Examiner * |
| MARCELO BERTOLETE CARNEIRO | Internal Examiner * |
| MARCOS TADEU DAZEREDO ORLANDO | Advisor * |
Summary: This work has developed a novel proposition for the strain-hardening equation. This proposition had its genesis in the phenomenological definition of the instantaneous strain-hardening exponent. The first part of the work describes a two step method for the determination of the strain hardening curves, when submitted to high levels of plastic deformation. For this purpose, the plastic behavior of an interstitial-free steel plate was evaluated in two steps. In the first stage, data from the symmetric biaxial expansion test, `Bulge test`, were used in conjunction with Hill`s quadratic yield criterion 48 to generate an effective strain-hardening curve,
or transformed data. In the second step the isotropic hardening laws or hardening equations were fitted to this data. The hardening equation that showed the best fit was the Swift-Hockett-Sherby (S-H-S) model. The results showed that the better the fit of a strain-hardening equation, the greater the tendency of its strainhardening curve to describe experimental instantaneous strain-hardening exponent curves. Based on this first part of the work a new constitutive model was developed to describe the stress-strain curve. The hypothesis was to construct an equation that was able to describe the instantaneous strain hardening exponent curve, presenting a better description of the strain hardening behavior of a given polycrystalline metal alloy. The strain hardening equation proposed in this work is based on the phenomenological definition of the instantaneous strain hardening
exponent. The constitutive equation is described by the product of two functions of polynomial exponential type. One is dimensionless and is responsible for generating the shape of the strain-hardening curve (true stress-true plastic strain curve), for a given polycrystalline metal alloy and is defined as the normalized strain-hardening function. The second gives in stress units the points on the curve generated by the normalized hardening function, and furthermore, enables the transformation/shifting of the hardening curve for different stress levels as a function of the boundary conditions. This function is defined as the strain hardening amplitude function. Both functions depend on the determination of the polynomial coefficients generated by fitting an interpolating polynomial to the experimental true stress-true plastic strain data on a natural logarithmic scale,
while only the strain hardening amplitude function depends on the values of true uniform elongation and true yield strength. An iterative method is proposed to determine for each metal alloy the amount of polynomial coefficients such that it minimizes the root mean square error (RMSE) between the experimental uniaxial
tensile data and the values predicted by the model. These polynomial coefficients are used to predict the instantaneous strain hardening exponent curve. In addition, from the strain hardening equation, it was possible to deduce a strain hardening rate equation, which uses the model predicted stress values and the instantaneous
strain hardening coefficient values. The model was validated to describe with excellent accuracy, based on mean square error and coefficient of determination values, the strain hardening behavior from experimental uniaxial tensile data on a duplex 2304 stainless steel alloy. The alloy showed parabolic shaped strainhardening curves and sigmoidal strain-hardening curves. The new strain hardening model was able to predict the strain hardening behavior of the sigmoidal and parabolic shaped curves of the lean duplex 2304 stainless steel alloy. Additionally, the model was able to describe with very good approximation the experimental curves of the incremental strain-hardening exponent and incremental strainhardening rate.
