Brittle materials stress-strain diagram

As discussed in Section 2.0 (Exploration), the earth s crust is part of a dynamic system and movements within the crust are accommodated partly by rock deformation. Like any other material, rocks may react to stress with an elastic, ductile or brittle response, as described in the stress-strain diagram in Figure 5.5. 

Figure 5.36 Comparison of typical stress-strain diagrams for ductile (top curve) and brittle (bottom curve) materials. Reprinted, by permission, from S. Somayaji, Civil Engineering Materials, 2nd ed., p. 24. Copyright 2001 by Prentice-HaU, Inc.

In terms of the mechanical behavior that has already been described in Sections 5.1 and Section 5.2, stress-strain diagrams for polymers can exhibit many of the same characteristics as brittle materials (Figure 5.58, curve A) and ductile materials (Figure 5.58, curve B). In general, highly crystalline polymers (curve A) behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation, as in... 

The strength properties of solids are most simply illustrated by the stress-strain diagram, which describes the behaviour of homogeneous brittle and ductile specimens of uniform cross section subjected to uniaxial tension (see Fig. 13.60). Within the linear region the strain is proportional to the stress and the deformation is reversible. If the material fails and ruptures at a certain tension and a certain small elongation it is called brittle. If permanent or plastic deformation sets in after elastic deformation at some critical stress, the material is called ductile. 

It is important to differentiate between brittle and plastic deformations within materials. With brittle materials, the behavior is predominandy 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 britde the material. 

Engineering materials are generally referred to as metallic and nonmetallic (ceramics and high pol5nners) materials, which are further classified as ductile or brittle. As shown in the stress-strain diagram in Figure 1.1, the strain of ductile materials is 100-1000 times larger than that of brittle materials. The... 

A typical stress-strain diagram for a composite material, in which strong and brittle fibres are reinforcing a ductile matrix, is shown in Figure 2.8, together with separate diagrams for fibres and matrix. The failure of a composite material occurs shortly after the failure of fibres and the post-failure behaviour of the matrix is highly non-linear. 

Typical stress-strain diagrams for brittle and ductile materials are shown in Fig, 2.7. For brittle materials such as cast iron, glass, some epoxy resins, etc., the stress strain diagram is linear from initial loading (point 0) nearly to rupture (point B) when average strains are measured. As will be discussed subsequently, stress and strain are point quantities if the correct mathematical definition of each is used. As a result, if the strain were actu-... 

Fig. 2.7 Stress-strain diagrams for brittle and ductile materials...

Ductile materials often have a stress-strain diagram similar to that of mild steel shown in Fig. 2.8 and can be approximated by a linear elastic-perfectly plastic material with a stress-strain diagram such as that given in Fig. 2.9(b). Failure for ductile materials is assumed to occur when stresses or strains exceed those at the yield point. Materials such as cast iron, glass, concrete and epoxy are very brittle and can often be approximated as perfectly linear elastic-perfectly brittle materials similar to that given in Fig, 2.9(a). Failure for brittle materials is assumed to occur when stresses or strains reach a value for which rupture (separation) will occur. 

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). ... 

The polymeric materials can be broadly classified in terms of their relative softness, brittleness, hardness, and toughness. The tensile stress-strain diagrams serve as a basis for such a classification (6). The area under the stress-strain curve is considered as the toughness of the polymeric material. Figure 2-4a... 

Fig. 4.3 Typical stress ((r)-strain (e) diagrams and parameters of various polymers in tensile test brittle plastics (a), ductile materials with yield stress (b and c), ductile materials without yield stress (d) and elastomeric materials (e) [13Gre].

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