Young stress-strain diagram

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

Finally, the modulus of elasticity E (Young s modulus), which is a measure of the stiffness of the polymer, can be calculated from the stress-strain diagram. According to Hooke s law there is a linear relation between the stress o and the strain e ... 

The graphic results, or stress-strain diagram, of a typical tension test for structural steel is shown in Figure 3. The ratio of stress to strain, or the gradient of the stress-strain graph, is called the Modulus of Elasticity or Elastic Modulus. The slope of the portion of the curve where stress is proportional to strain (between Points 1 and 2) is referred to as Young s Modulus and Hooke s Law applies. 

Young s modulus, also referred to as elastic modulus, tensile modulus, or modulus of elasticity in tension is the ratio of stress-to-strain and is equal to the slope of a stress-strain diagram for the material. In the standard test method, ASTM D412, a force is apphed to a dog-bone-shaped sample of the cured adhesive. The force at elongation (strain) is measured. Most often, the elongation is 25-30% although for elastomeric materials it may be 100% or greater. 

Young s Modulus. Young s moduli, E, for several resins are plotted vs. temperature in Fig. 7. Young s moduli were determined from stress-strain diagrams. At 4K, their values are within 10%. Therefore, the low-temperature values of E do not depend markedly on the detailed chemical structure. It must be emphasized that epoxy resins are energy-elastic and have a nearly linear stress-strain behavior to fracture at low temperatures. No rate dependence was found over several decades. This is not true for many high polymers, such as polyethylene (PE), which are not cross-linked. PE behaves viscoelastically, even at 4 K [%... 

From what has already been diseussed in the sections above, it is sufficiently clear that all eharacteristie parameters derived from a stress-strain diagram (Young s modulus, (upper and lower) stress at yield and elongation at yield, stress at break and elongation at break) are functions of the deformation rate, test temperature and imposed state of stress. 

The ceramics are materials that demonstrate brittle fractxxre, this means presenting only elastic stress behavior. Stress-strain diagram is therefore a straight line whose slope is Young s modulus of the material. The temperature dependence of the stress-strain diagram is therefore related to the dependence of Young s modulus. 

Polymers typically behave viseo-elastically, that is their mechanical properties are time and temperature dependent. However, the properties mentioned above are measured almost instantaneously and it is assumed that the material behaves elastieally, or more importantly linear elastic if a Young s modulus is considered. In Figure 7.5, typieal stress-strain diagrams are shown for brittle, plastic and highly elastomeric behaviour, as observed in many synthetic polymers. This behaviour is dependent on temperature as well as the amount of plasticizer (or other additives). ... 

Hence, for out-of-plane loading Young s modulus for the hollow composite increases when the cell wall becomes thicker and when the wall length is shorter. Figure 3.8 shows the schematic diagrams by Gibson and Ashby (1999) of the strain-stress curves... 

E and A are Young s modulus and cross-sectional area of the fibre, respectively, is the uniform matrix strain, G is the shear modulus of the matrix. Corresponding diagrams of bond stress t and tensile stress a in the fibre are shown in Figure 8.11. Values of the tensile stress a (x) in the fibre are obtained directly from equation (8.9). 

---