Question

A torsion test is performed on an aluminum probe, with the following results given in the following table:

(degress(º))	0	5	10	15	20	25	30	35	40	45	50	55	60	80
T kgf.m	0	5	11	14	14.5	14.7	16.3	16.4	16.5	16.6	16.7	16.4	16.5	16

The probe dimensions are as follows:

Length(L)	Diameter(D)
180	10

Through your graph of behavior of shear to torsion against angular deformation determine the following:

• Limit proportional to the cut

• Shear creep (0.2% deformation)

• Maximum resistance shear
• rigidity modulus (G)

• Cut Resilience Module

 Failure type (malleable, ductile, tenacious or brittle)

Answer 1

T= torque.

J= polar moment of inertia.

for shaft J=

r= radius of shaft=0.005m.

=shear stress.

G= rigidity modulus.

= angle of twist in radians.

l= length of shaft =0.18m.

=shear strain=

From the values given for in radians.

=0 , =0.

=0.087 , =0.0024.

=0.174 , =0.0048.

=0.261 , =0.0096.

=0.349 , =0.012.

=0.523 , =0.014.

From the values given for T in Nm, in GPa.

T=0, =0.

T=49.03, =0.224.

T=107.87, =0.549.

T=137.24, =0.699.

T=142.2, =0.724

T=144.16, =0.734

T=159.85, =0.814.

(a)Limit of proportionality ,LOP is upto =0.224GPa.

(b)Shear creep(0.2% deformation) =0.725GPa.

(c)Maximum resistance shear = top point on the curve= 0.814GPa.

(d)Modulus of rigidity G= / = 0.224 */0.0024=93.33GPa.

(e)Modulus of resilance=area in the graph upto LOP =0.5*0.0024*0.224 =0.000268.