Master_In-Class_Mid-term_2010_solutions - EMA 6715...

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Unformatted text preview: EMA 6715 Mid—term Examination [Part 1] October 21, 2010 Name W»? S’ 772/1}, Closed book examination. If you think that one or more of your answers needs clarification, please write on reverse side citing the question number. 1. The Eulerian infinitesimal strain components, eij are related to the displacement and position vectors by the following equation: (.9 r: (2 <35: ,9 ) 2. The components of a displacement vector are 111 = 0.004X1 - 0. 16x12, u2 = 0.024X2, 113 = 0.025 X3 a. What is the value for en? ('3’). (:W 4’ b. What is the value for 8 12 m c"), 0 c. What is the value for (021 C7 . a» d. What is the value for AV/V (5'9, 6:: f)” I? e. One of the principal strain values is m (.9 , ,2 jg / a“; (:9. (4? 3. Answer the following questions: Q a. 51d aklbklmn is a Q m a order tensor. b. Simplify 5U XJ- j?“ A p f, {w 1/? c. Give 2 properties of symmetric second order tensors 3 (inflame/K; SH)” ins/2'4 '7étrmr/2izmp W I; flew/f [firm/f 7.42%] 274m¢ww {Jr “W. if) of Ax t; 01.4? CJV’flw/r ; / a W . fly 5. To solve 2D elastic problems the Airy stress function is often used. This function must satisfy the boundary conditions and the AM mam , (f equation. This latter equation combines Hooke’s Law with the Cow/W {5452/1 and f Mam equatiOYls. 6. For a cubic crystal, the stiffness constants are: 01 120222033, c12=c13=cz3 and 04420552066, the rest = O. The compliance constants, Sjj have the same symmetry. Write the general form of Hooke’s Law for the following components in terms of the elastic constant: 82: 312, “)t wi‘ SH 6:1. 4” 5‘12. 0'5 2 €75” 03: gig El 5 ‘5“ Ca; Q} i“ Cu (:53 If the material is tested in tension (01), then 81 = 5:, CT] 9.0.57?) 7. The maximum Young’s modulus for a cubic crystal is either along 4 / a? 0 ‘> or «in / 4» directions. In terms of compliance constants, Young’s modulus. for a principal direction is ’2 S! ,7 and Poisson’s ratio for a principal direction is “r 5" l/SH . ' 8. The value of the bulk modulus for a material depends on the (:7 u rz ya new of the interatomic potential at the ((30 . l“. 6/219 Ly. interatomic spacing. 9. Which of the following has the greatest theoretical fracture stress? SiC, Si3N4, SiOg? S” a‘ C, . 10. Which of the following has the greatest bulk modulus, Asz03, AszS3, AszSe3, or AszTe3? 45 g (Q;- .. Name m yr] Q "2’32 (3... 11. For carbides, the bu1k modulus ([25: [62.3,ng with increasing equilibrium spacing or with / [I] <5 . atomic volume. \i 12. The isotropic elastic constants of particulate composites can be estimated without any assumption of particle shape. Sometimes, values greater than the upper bound estimate can be measured. What is a possible reason? Vlé " dig-cm? %W417 13. The Griffith criterion for failure considers the total energy, U, of a cracked body with changes in crack length, 0. The failure criterion based on Griffith’s approach is usually written as: a? If .. é. a a" 2H ( . 6.. :2; w 2 «52,6 2 w J 14. The crack extension force or strain energy release rate depends o the work done by the applied loads, W, and the change in the elastic energy of the system, UE, such that an? L1} 5"“ W ‘t‘"‘4’€e’) [equation]. -, “"””’““’“Zi‘“2§f 15. The stress intensity factor describes the W fl/r lira/Zr..- of the stresses near a crack tip and is related to the applied stresses by K = j (17}, 16. Name three (non-indentation) techniques that are used to measure fracture toughness (ycaw/tfixg/rf”éw var/e f 559' N13 f Z) TWO)? 0%LE. mix/VA) ‘ DC 5 17. For an elliptically shaped crack, the stress intensity factor is a minimum at the end of the 5' W41wa axis. 18. In a beam subjected to bending, the 3%)a IQ ,Qg,’ are dependent on the material properties and the :5 are independent of the material properties. 19. A plate that is thin can most like be analyzed using plane 5; Lg [stress or strain]. 20. The stress concentration factor is for a sharp crack than a spherical pore 21. If a particle in a matrix has a thermal expansion coefficient less than that of the matrix, then cracks can form upon cooling. If these cracks form, where are the possible locations? rug/{baa 14; mm 717m" x 22. What is the stress state of the particle in Question 21? (50 I/H/r/x/ypm 23. What is the stress state in the matrix of Question 21‘? {1' a from [hmwéhéfl fingzm) rim/9r €19 M/gmflmiama 24. The theoretica1 strength of a material can be estimated from a sinusoidal stress-displacement function in which the period is M2 where 9» is the wavelength of the sine function. The integration of the stress-displacement curve from O to M2 determines the surface energy. Why is the integration from O to M2 [ as opposed to M4]? 7% 3L?:"«Q4¢LW% If Mr} gage mafia Mae firm/me avg/9&1” we-.. 25. Which of the following type of defects that can lead to failure is least severe: pores, inclusions or surface cracks? ’ [MC/Mg‘ra‘mvg 432137;) ...
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Master_In-Class_Mid-term_2010_solutions - EMA 6715...

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