EMA 4223                                                                              April 2007

Mechanical Behavior                                                                Test 5A

 

Name ___________________________                                UFID # ____________________

[Each Question is worth 20 points unless noted otherwise.]

 

1. A client asks you to determine the expected (fast fracture) tensile strengths for silica glass optical fibers of 1000 m lengths (diameter 100 microns) when they have the results of  tensile tests for 1 m lengths (same diameter).  The results are as follows:  0.7 GPa, 1 GPa, 0.5 GPa, 0.6 GPa and 0.6 GPa, 0.8 GPa and 2 GPa.  From the literature, they know the Weibull modulus, m = 10, elastic modulus, E =70 GPa and KIC = 0.75 MPa m1/2.  What are the expected strengths, corresponding to the 1 m lengths, for the fibers at 1000m lengths assuming Weibull statistics apply and no other factors are involved?        [Your answer will be 7 strength values.]

 

 

 

 

 

 

 

 

 

 

2.   A thin walled (cylindrical) pressure vessel 2.00 cm thick originally contained a semi-circular crack with radius 0.25 cm located at the inner surface and oriented normal to the hoop stress direction.  Repeated pressure cycling allowed the crack to grow larger.  If the fracture toughness of the material is 50 MPa m1/2, the yield strength is 800 MPa, and the hoop stress is 300 MPa, would the vessel leak before break? [ Use a Y factor of 1.1 ] [sH = p r/t].

 

 

 

 

 

 

 

 

 

 

3. An infinitely large plate is subjected to a gross stress of 300 MPa.  There is a central crack 2a =  20/p cm long and the material has a yield strength of 750 MPa.

(a)         Calculate the stress-intensity factor at the tip of the crack.

(b)        Calculate the plastic zone size at the crack tip.

(c)         Comment on the validity of the plastic zone correction by calculating the effective stress intensity factor and comparing to that in (a), assuming that the plate fractures at 300MPa.

 

 

 

 

 

 

 

4a. Match column A with the most appropriate words or phrase from column B.

 

            A.                                                                               B.

plastic zone size      ___________                                (a) usually thick sections

fracture toughness      _________                                 (b) effect of crack geometry on crack-tip stress

stress intensity            _________                                 (c) out of plane shear loading

plane stress                 __________                              (d) material property

plane strain                 __________                              (e) region of plasticity near crack tip

leak before break      __________                               (f) scale factor for crack-tip stress field

Mode I                   ____________                              (g) usually thin section

Mode II                  ____________                             (h) tensile loading on crack

Mode III               _____________                             (i) in-plane shear loading

stress concentration factor ______                                (j) 2a = 2t

4(b) .  Match the following phrases or names with the most appropriate letter from the accompanying figures and circle whether the figure represents primarily a brittle (B) or ductile (D) type failure. 

 

i.    Microvoid coalesence under tensile loading ____________________.        D     B

ii.   chevron markings in a metal ________________________________.                   D     B

iii.  microvoid coalesence under shear loading _____________________.                    D     B

iv.  intergranular fracture ______________________________________.                  D     B

v.   transgraular fracture _______________________________________.                D     B

vi.  twist hackle markings on fracture surface ______________________.                   D     B

vii. fracture surface of glass/crystal regions in a polymer ­­­­­­_____________.                     D     B

viii.fracture showing mirror-mist & hackle zones ___________________.                    D     B

ix.  failure by shear in a pure metal ______________________________.                   D     B

x.   crazing in a polymer  ______________________________________.                 D     B 

 

5.  As a materials engineer you are required to design a glass window for a vacuum chamber.  The opening can be adjusted for a circular disc of radius R and thickness t.  It is freely supported in a rubber seal around its periphery and subjected to a uniform pressure difference Dp = 0.1 MPa. The window is a critical component and requires a failure probability of 10-6.  The design life of the component is 1000 hours.  The modulus of rupture tests of the glass discs to be used resulted in a mean strength of 300 MPa in a short term (60 second ) bending test.  What are the permissible dimensions for this window?  [Assume Poisson’s ratio is 0.25, the Weibull’s modulus is 10 and the stress corrosion susceptibility parameter is 5.  Assume the elastic modulus is 70 GPa and KIC = 0.75 MPa m1/2 .  Further, assume the maximum stress in the plate is smax ~ Dp R2 / t2].