Question

Using expressions 2.29a and 2.29b from the textbook, plot normal stress (σθ) and shear stress (τθ) versus angle of an inclined stress element for a bar loaded by axial forces. Use Matlab or Excel. What are slip bands? Why slip bands occur when mild steel bars are loaded in tension. Explain your answer using the plotted graphs.

results in the following expressions for the normal and shear stresses: (2-29a) (1 2 cos 20) (sin 20) 2 (2-29b) O sin 0 cos 0 T x on an inclined section oriented at an These equations give the stresses acting angle 0 to the x It is important to recognize that Eqs. (2-29a and b) statics, and therefore they tions are valid for any material, whether it behaves linearly elastically or inelastically axis (Fig. 2-55). were derived only from independent of the material. Thus, these equa- are nonlinearly, or Using expressions 2.29a and 2.29b from textbook, plot normal stress (oe) and shear stress (te) angle of an inclined stress element for a bar loaded by axial forces. Use Matlab or Excel versus What are slip bands? Why slip bands occur when mild steel bars are loaded in tension. Explain your answer using the plotted graphs

Answer 1

to draw the graph first we have to understand the question calculation that what the question want to ask lets start the the work with given data..

Given data:

as there is an stress element which is loaded by only axial force due to witch stress are developed,are different in different inclined plane.

figure 1

Figue1 stress element if we consider dimension (length, width, height) and amount of axial force the we calculate stress as sigma = force/cross-section so we direct assume the stress. For simplicity expression sigma theta = sigma x cos^theta z theta = -sigma/2 sin 2 theta (here negative sign in shera stress indicate direction of shear stress on inclined plane is opposite to assumed.

as per given equation we calculate the few data to plot the graph which is shown in excel sheet.

before drawing the graph first we have to consider some data such as dimension of stress element and amount of axial force from this we calculate the normal stress acting on the plane or for simplicity we can direct assume the amount of normal stress direct as showen in figure

figure 2

Graph between normal stress and inclined angle thita.

Graph between shear stress and inclined angle thita.

Slip band are commonly known as plastic deformation which is generaly occure in low carbon containig matel like mild steel, aluminium during tension test.

during tensile test on mild steel after crossing elatic limit (point B) we come to an point name upper yield point (point C) at that point carbon atom which are present in mild steel in low concentrate, start to move or they get sliped to void which is present in mild steel due to presence of carbon atom. and this cause sudden decrease in strength which ultimately indicate plastic deformation so slip band are also known as plastic deformation(region CD in graph).

graph

in the graph

HTS means high tensile steel or carbon atom concentration is more in this.

reason behind this is only presence of carbon which which is an impurity for this and it create some void in it.