Strength and failure theories

Question 1

What characterizes the longditudinal tensile strength X_t?

Answer 1

• Strength is dominated by the fiber tensile strength
• Failure is sudden and brittle

Question 2

What characterizes the transverse tensile strength Y_t?

Answer 2

• Strenght dominated my the matrix properties and the fiber-matrix interface bonding strength
• Ususllly brittle failure mode

Question 3

What has the highest strength of transverse compressive strength (Y_c) and transverse tensile strength (Y_t)?

Answer 3

Transverse compressive strength Y_c is typically much greater. Often by a factor of 3-4 or more.

Question 4

What is the load propotionality factor R?

Answer 4

• R = 1/f
• The factor of how many times we can increase the load before failure

Question 5

What is the meaning of the exposure factor f_E?

Answer 5

• How much load has been “used” relatively to the strength.
• f_E = load/strength
• f_E = 1/R

Question 6

What is the relationship between the load propotionality factor (R) and the exposure factor (f_E)?

Answer 6

R*f_E = 1

Question 7

In general, how is a failure criterion expressed?

Answer 7

Question 8

What is the basic idea of the Maximum stress criterion?

Answer 8

Comparison of the individual stres components to the induvidual strength components.
Failure when f ≥ 1

Question 9

Why should shear stresses be considered as absolute value in any stress based failure crieria?

Answer 9

Materials typically have symmetric properties with respect to shear stresses, meaning they cannot distinguish between positive and negative shear.
-> If τ < 0, f would always be < 0.

Question 10

In general, how can we find the exposure factor if we have a failure function f?

Answer 10

Multiply all the stresses by R and solve for R.
f_E = 1/R

Question 11

How to derive the parameters in the Tsai-wu criterion?

Answer 11

Set all the stresses to be zero except for one to be equal to the strength (tensile and compressive), i.e:
σ_1= X_T and σ_1 = - X_t, all others = 0.
Substitude σ for X_T and -X_T and solve for F values. (2 equations and 2 unknowns)

Question 12

How can we find the load proponality factor (R) for the tsai-wu failure criterion?

Answer 12

Multiply all the stresses by R, and solve f as a quadratic formula:
aR^2 + bR + c = 1

Question 13

What are the basic strength parameters X_T, X_C, Y_T and Y_C from this Tsai-Wu envelope?

Answer 13

Question 14

What are the coefficients are expressed by the basic strength parameters for the Tsai-Wu criterion?

Answer 14

Question 15

What is the general equation for an ellipse?

Answer 15