DESIGN OF LAMINATES 



6-3 



loading a test specimen to rupture, usually in tension, measuring the strain at various stress 

 levels and plotting the results. The two most important characteristics obtained from the 

 tensile test are strength and ductility. Speed of testing, preloading, form and cross-section 

 shape will considerably affect the properties of a material. 



Figs. 6-1, 6-2 and 6-3 are typical stress-strain curves for metals, wood and fiber- 

 glass laminates. The curves have several points of inflection and each point is indicative of 

 a specific change in the behavior of the material. From these points of inflection, properties 

 such as proportional limit, yield point, initial and secondary moduli of elasticity and point 

 of rupture or ultimate stress can be determined. 



Fig. 6-1 indicates the variation in the stress-strain behavior for some commonly used 

 structural metals. The first part of the curves in Figs. 6- la, 6- lb and 6-lc are substan- 

 tially a straight line to point P, the proportional limit. This indicates a constant ratio 

 between the stress and strain, and within this range the material behaves elastically con- 

 forming to Hooke's Law of Proportionality. The numerical value of the ratio is the modulus 

 of elasticity, E, and is determined by dividing the unit stress by the unit strain. 



E - IS 



(6.1) 



Where E = Modulus of Elasticity - psi 



f+ = Unit stress - psi 



e = Unit strain - inches per in. 



Beyond the proportional limit, the ratio 

 of the stress to strain, designated as the 

 tangent modulus, varies with the slope of the 

 stress-strain curve and is usually different 

 at each stress value. 



The curve in Fig. 6-lc shows two 

 separate proportional limits and moduli of 

 elasticity; initial and secondary. This curve 

 indicates the behavior of clad aluminum alloys 

 where the initial modulus holds up to the 

 proportional limit of the relatively soft 

 covering and the secondary modulus holds up 

 to the proportional limit of the stronger 

 core material. 



ILE STRESS 



a. MATERIAL HAVING A DEFINITE 

 YIELD POINT (SUCH AS SOME STEELS) 



STRAIN - INCHES PER INCH 



ULTIMATE TENSILE STRESS 



b. MATERIALS NOT HAVING A 

 DEFINITE YIELD POINT (SUCH AS 

 ALUMINUM ALLOYS, MAGNESIUM, 

 AND SOME STEELS) 



INCHES PER INCH 



I P 2 



S P 1 



STRAIN - INCHES PER INCH 



REFERENCE 4 



Fig. 6-1. Typical Tensile Stress- 

 Strain Curves for Metals 



Beyond the proportional limit, the strain 

 increases at a faster rate with increased 

 stress, and slightly above this limit the 

 material begins to retain a permanent set 



upon removal of the stress. For some steels, a sharp break in the curve occurs at a stress 

 considerably below the ultimate tensile stress, Fig. 6- la. At this stress, referred to as 

 the yield point on the curve, the material breaks down rapidly and a sudden large increase 

 in deformation occurs with little or no increase in stress. Nonferrous metals and some 

 steels do not have this sharp break or yield point but yield gradually after passing the pro- 

 portional limit, Figs. 6- lb and 6-lc. 



