Page 223 - Mechanical Behavior of Materials

Problems and Questions 225

(b) Nomenclature for Stresses and Strains
x, y, z Coordinate axes identifying directions for stresses and strains
γ xy , γ yz , γ zx Shear strains
ε x , ε y , ε z Normal strains
ε c Creep strain
ε e Elastic strain
ε p Plastic strain
ε sc , ε tc Steady-state and transient creep strains, respectively
σ x , σ y , σ z Normal stresses
τ xy , τ yz , τ zx Shear stresses

(c) Nomenclature for Orthotropic and Composite Materials
X, Y, Z The particular x-y-z coordinate axes that are aligned with the
planes of material symmetry.
E X , E Y , E Z Elastic moduli in the X-, Y- and Z-directions.
G XY , G YZ , G ZX Shear moduli in X-Y, etc., planes.
m, r Subscripts indicating matrix and reinforcement materials, res-
pectively.
V m , V r Volume fractions for matrix and reinforcement materials, res-
pectively.
ν XY , etc. Poisson’s ratio giving the transverse strain in the Y-direction due to
astressinthe X-direction; others similarly.

REFERENCES

BRINSON,H.F., andL.C. BRINSON. 2008. Polymer Engineering Science and Viscoelasticity: An Introduction,
Springer, New York.
GIBSON, R. F. 2004. Principles of Composite Material Mechanics, 2d ed., McGraw-Hill, New York.
MCCLINTOCK,F. A., and A. S. ARGON, eds. 1966. Mechanical Behavior of Materials, Addison-Wesley,
Reading, MA.
R ¨ OSLER,J., H. HARDERS,and M. B ¨ AKER. 2007. Mechanical Behavior of Engineering Materials, Springer,
Berlin.
TIMOSHENKO, S.P., andJ.N. GOODIER. 1970. Theory of Elasticity, 3d ed., McGraw-Hill, New York.

PROBLEMS AND QUESTIONS

Section 5.2
5.1 Define the following terms in your own words: (a) elastic strain, (b) plastic strain, (c) creep
strain, (d) tensile viscosity, (e) recovery, and (f) relaxation.
5.2 An aluminum alloy is represented by the elastic, perfectly plastic model of Fig. 5.3(b), with
constants E 1 = 80 GPa and σ o = 250 MPa.