WJEC Physics for AS: Study and Rev Guide

Grade boost Using your calculator: Enter 100 M(Pa) as 100 × 10 6 and 70 G(Pa) as 70 × 10 9 . Pointer Brittle materials have no mobile edge dislocations because: 1. they are amorphous (no regular lattice),e.g. glasses, or 2. they are ionically or covalently bonded, e.g. ceramics, or 3. they are metallic but have very small crystals with large numbers of impurities, e.g. cast iron. Pointer Masonry is very weak in tension – especially the mortar joints. Old churches were built with towers at the corners of the walls. The weight of these helps keep the walls in compression. QUICKFIRE QUICKFIRE s A glass fibre of diameter 0.12 mm just breaks when a mass of 650 g is hung from it. Its Young modulus is 80 GPa. (a) Calculate the UTS. (b) Calculate the strain at fracture. (c) Sketch the stress– strain graph. Answer E = , so = ε x = = = 0.00143 70 GPa 100 MPa ε σ E σ x \ Δ l = ε x l 0 = 0.00143 × 60 cm = 0.086 cm (2 s.f.) Note that we don’t need to convert l 0 to m: the unit of D l is the same as the unit of l 0 . (b) Brittle fracture The tensile breaking stress of brittle materials is a lot lower than predicted from the strength of the bonds within the material, e.g. the theoretical UTS of glass ~ 6 GPa against the experimental value of up to 0.1 GPa for bulk glass. The material fractures because of the existence of microscopic cracks in the surface and these are responsible for the weakness of brittle materials under tension. Fig. 1.5.17 shows a brittle sample with highly exaggerated crack. The dotted lines are so- called stress lines , which indicate how the tension is transmitted through the specimen. The stress lines are concentrated around the tip of the crack, magnifying the stress. There are no mobile edge dislocations to relieve the stress (see Pointer) so the crack breaks further at the tip, which produces an even higher stress at the new tip. The result is catastrophic failure: the crack propagates rapidly through the material. Experiments on thin glass fibres have shown that, if care is taken not to damage the surface, the UTS of a freshly drawn glass fibre increases with decreasing diameter. The thinner the glass fibre, the smaller the thermal stresses when it cools, so the problem with surface cracks is less. Very thin ( ~ 1 m m) glass fibres have strengths approaching the theoretical value. (c) The structural use of brittle materials Brittle materials can be used in engineering if the propagation of cracks can be avoided. This is done in the following ways: 1. Concrete and brick structures are designed so that the brittle material is always under compression . In this way the cracks do not open up. 2. Pre-stressed concrete is made by pouring the concrete around steel rods under tension. The rods are slackened off when the concrete has cured, putting the concrete under compression. 3. Pre-stressed glass is manufactured so that the surface is under compression. This is done by a rapid cooling of the surface – the surface then sets first and the later cooling of the core puts the surface under compression. A tension can be applied without the crack-bearing surface being put under tension. Fig. 1.5.17 Brittle failure Crack 58 AS Physics: Study and Revision Guide