Write a Matlab Program which computes and plots ENGINEERING stress vs. ENGINEERI

Question

Write a Matlab Program which computes and plots ENGINEERING stress vs. ENGINEERING strain for a uniaxial tension test of hot-rolled AISI 1020 steel (mechanical engineering)

Take the minimum and maximum true strains to be 0.0001 and 0.92

The TRUE stress vs TRUE strain diagram is below, you will need to convert to ENGINEERING stress vs strain

Elastic region Transition region Plastic strain-strengthening region . 200 = 0.92 115 100 80 115 KS 60 30 10 3 4 5 6 780.1 2 3 4 56 78 1.0 2 3 4 56 78 10 2 3 4 5678100 True strain ET1% (log) FIGURE 3.3 True-stress-true-strain curve-hot-rolled 1020 steel (corresponds to Figs. 3.1 and 3.2).

Explanation / Answer

Assume that the initial cylindrical sample dimensions are: radius = 1.0 in., length = 5.0 in.

Matlab Code:

clc; clear;

% Define the input values

% Radius in [in]
R0 = 1.0;

% Length in [in]
L0 = 5.0;

% Minimum true strain [-] and true stres [ksi]
eMin = 0.0001;
sMin = 10.0;

% True strain at failure[-] and true stress [ksi]
eMax = 0.092;
sMax = 110;

% Elastic limit
eEL = 0.0015;
sEL = 40;

% Plastic limit
ePL = 0.008;
sPL = sEL;

% Strain hardening coefficient
s0 = 115;
m = 0.22;

% Deflection
% eT = ln(L/L0) -> L = L0 * exp(eT) -> dL = L - L0 = L0 * [exp(eT) - 1]

% Load
% pi * R0^2 * L0 = pi * R^2 * L i.e. A0 * L0 = A * L
% A = A0 * L0/L = A0 / exp(eT)
% F = sT * A

A0 = pi * R0^2;
i = 1;
mEL = (sEL - sMin) / (eEL - eMin);

for eT = [eMin: eMin * 2: eMax]
dL(i) = L0 * (-1 + exp(eT));
A = A0 / exp(eT);
  
if (eT <= eEL)
F(i) = mEL * (eT - eMin) * A;
  
elseif ((eT > eEL) & (eT <= ePL))
F(i) = A * sPL;

else
F(i) = A * s0 * eT^m;
end
i = i + 1;
end

plot(dL, F, "linestyle", "-", "linewidth", 2);
xlabel('deltaL [in]'); ylabel('F [kip]');

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