Can someone help me with this MATLAB problem? The yield strength, o, of many met

Question

Can someone help me with this MATLAB problem?

The yield strength, o, of many metals depends on the size of the grains. For these metals, the relationship between the yield stress and the average grain diameter d can be modeled by the Hall Petch equation: Go The following are results from measurements of average grain diameter and yield stress. d (mm) 0.005 0.009 0.016 0.025 0.040 0.062 0.085 0.110 (MPa) 205 150 135 97 70 80 (a) Using curve fitting, determine the constants oo and k in the Hall-Petch equation for this material. Using the constants determine with the equa- tion the yield stress of material with a grain size of 0.05 mm. Make a plot

Explanation / Answer

Executable code:

d=[0.005 0.009 0.016 0.025 0.040 0.062 0.085 0.110];
S=[205 150 135 97 89 80 70 67];
z=polyfit(d^(-0.5),S,1);
k=z(1);
S0=z(2);
fprintf('The constants S0 and k in the Hall-Petch equation are %6.2f and %6.2f/n',S0,k)
S0= S0+k*0.05^-0.5;
fprintf(The yield stress of the material with a grain size of is %6.2f ',S0)
d1=[0.005:0.005:0.11];
S1=S0+k*d1^-0.5;
plot(d,S,'o')
hold on
plot(d1,S1,'g')
title('Yield stress vs Average grain diameter using cure fitting')
xlabel('Average grain diameter (mm)')
ylabel('Yield stress (MPa)')

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