双语课计算部分.doc

所有的题目都在课件里面大家有空还是多看看课件吧！很多重复的题目，删掉了仅供参考哈！ 三、分析或计算1. Silicon carbide particles are compacted and fired at a high temperature to produce a strong ceramic shape. The specific gravity of SiC is 3.2 g/cm3. The ceramic shape subsequently is weighed when dry (360g), after soaking in water (385 g), and while suspended in water (224 g). Calculate the apparent porosity, the true porosity, and the fraction of the pore volume that is closed.The closed-pore percentage is the true porosity minus the apparent porosity, or 30 - 15.5 = 14.5%. Thus2 The flexural strength (弯曲强度) of a composite material reinforced with glass fibers is 45,000 psi and the flexural modulus is 18 106 psi. A sample, which is 0.5 in. wide, 0.375 in. high, and 8 in. long, is supported between two rods 5 in. apart. Determine the force required to fracture the material and the deflection of the sample at fracture, assuming that no plastic deformation(塑性变形) occurs.3. Assume that an advanced ceramic, Sialon (acronym for silicon aluminum oxy-nitride), has a tensile strength of 60,000 psi. Let us assume that this value is for a flaw-free ceramic. (in practice, it is almost impossible to produce flaw-free ceramics.) A thin crack 0.01 in. deep is observed before a Sialon part is tested. The part unexpectedly fails at a stress of 500 psi by propagation of the crack. Estimate the radius of the crack tip. 4 A chain used to hoist heavy loads fails (提升重物的链断裂失效). Examination of the failed link indicates considerable deformation and necking prior to failure. List some of the possible reasons for failure.Solution 1. The load exceeded the hoisting capacity of the chain. Thus, the stress due to the load exceeded the yield strength of the chain, permitting failure. Comparison of the load to the manufacturers specifications will indicate that the chain was not intended for such a heavy load. This is the fault of the user! 2. The chain was of the wrong composition or was improperly heattreated. Consequently, the yield strength was lower than intended by the manufacturer and could not support the load. This may be the fault of the manufacturer!5. . A titanium pipe used to transport a corrosive material at 400 is found to fail after several months. How would you determine the cause for the failure?Since a period of time at a high temperature was required before failure occurred, we might first suspect a creep or stress-corrosion mechanism for failure. Microscopic examination of the material near the fracture surface would be advisable. If many tiny, branched cracks leading away from the surface are noted, stress-corrosion is a strong possibility. However, if the grains near the fracture surface are elongated, with many voids between the grains, creep is a more likely culprit.6 An aluminum rod is to withstand（经受） an applied force of 45,000 pounds. To assure a sufficient safety(足够的安全), the maximum allowable stress on the rod is limited to 25,000 psi. The rod must be at least 150 in. long but must deform elastically no more than 0.25 in. when the force is applied. Design an appropriate rod.7 We produce good chemical resistance in a glass when we introduce B2O3 into silica. To assure that we have good glass-forming tendencies, we wish the O:Si ratio to be no more than 2.5, but we also want the glassware to have a low-melting temperature to make the glass-forming process easier and more economical. Design such a glass.Let us determine the amount of B2O3 we must add to obtain exactly an O:Si ratio of 2.5. Let fB be the mole fraction of B2O3 added to the glass, and (1 fB) be the mole fraction of SiO2:Therefore, we must produce a glass containing no more than 14.3 mol% B2O3. In weight percent:8 Design a supporting 3-in.-wide plate made of sialon, which has a fracture toughness of 9,000 psi , that will withstand a tensile load of 40,000 lb. The part is to be nondestructively tested (非破坏性的实验)to assure that no flaws are present that might cause failure.9 An engineer investigating the cause of an automobile accident finds that the right rear wheel has broken off at the axle. The axle is bent. The fracture surface reveals a Chevron pattern pointing toward the surface of the axle. Suggest a possible cause for the failure.The Chevron pattern indicates that the wheel was subjected to an intense impact blow, which was transmitted to the axle, causing failure.Further examination of the fracture surface, microstructure, composition, and properties may verify that the axle was manufactured properly.10 The flexural strength of a composite material reinforced with glass fibers is 45,000 psi and the flexural modulus is 18 106 psi. A sample, which is 0.5 in. wide, 0.375 in. high, and 8 in. long, is supported between two rods 5 in. apart. Determine the force required to fracture the material and the deflection of the sample at fracture, assuming that no plastic deformation occurs. (计算部分同第二题)Design requirements to be met by the sledgehammer. A partial list 1. The handle should be light in weight, yet tough enough that it will not catastrophically break. 2. The head must not break or chip during use, even in subzero temperatures. 3. The head must not deform during continued use. 4. The head must be large enough to assure that the user doesnt miss the fence post, and it should not include sharp notches that might cause chipping. 5. The sledgehammer should be inexpensive.11 A large steel plate used in a nuclear reactor has a plane strain fracture tough ness of 80,000 psi and is exposed to a stress of 45,000 psi during service. Design a testing or inspection procedure capable of detecting a crack at the edge of the plate before the crack is likely to grow a t a catastrophic rate (Assuming f = 1.12).12 Suppose 2 wt% ThO2 is added to nickel. Each ThO2 particle has a diameter of 1000 . How many particles are present in each cubic centimeter?( The densities of ThO2 and nickel are 9.69 and 8.9 g/cm3, respectively)The volume fraction is:Therefore, there is 0.0184 cm3 of ThO2 per cm3 of composite. The volume of each ThO2 sphere is:13 Design a unidirectional fiber-reinforced epoxy-matrix strut having a round cross-section. The strut is 10 ft long and, when a force of 500 pounds is applied, it should stretch no more than 0.10 in. We want to assure that the stress acting on the strut is less than the yield strength of the epoxy matrix, 12,000 psi. If the fibers should happen to break, the strut will stretch an extra amount but may not catastrophically fracture. Epoxy costs about $0.80/lb and has a modulus of elasticity of 500,000 psi.For high modulus carbon fibers, E = 77 106 psi; the density is 1.9 g/cm3 =0.0686 lb/in.3, and the cost is about $30/lb. The minimum volume fraction of carbon fibers needed to give a composite modulus of 14.5 106 psi is:The volume fraction of epoxy remaining is 0.817. An area of 0.817 times the total cross-sectional area of the strut must support a 500-lb load with no more than 12,000 psi if all of the fibers should fail:Although the carbon fibers are the most expensive, they permit the lightest weight and the lowest material cost strut. (This calculation does not, however, take into consideration the costs of manufacturing the strut.) Our design, therefore, is to use a 0.255-in.-diameter strut containing 0.183 volume fraction high modulus carbon fiber. 14 A high-strength steel plate (Figure 7-19), which has a plane strain fracture toughness of 80 MPa , is alternately loaded in tension to 500 MPa and in compression to 60 MPa. The plate is to survive for 10 years, with the stress being applied at a frequency of once every 5 minutes. Design a manufacturing and testing procedure that assures that the component will serve as intended.Solution15 A cemented carbide cutting tool used for machining contains 75 wt% WC, 15 wt% TiC, 5 wt% TaC, and 5 wt% Co. Estimate the density of the compositeFirst, we must convert the weight percentages to volume fractions. The densities of the components of the composite are:From the rule of mixtures, the density of the composite is16. A silver-tungsten composite for an electrical contact is produced by first making a porous tungsten powder metallurgy compact, then infiltrating pure silver into the pores. The density of the tungsten compact before infiltration is 14.5 g/cm3. Calculate the volume fraction of porosity and the final weight percent of silver in the compact after infiltration.From the rule of mixtures:After infiltration, the volume fraction of silver equals the volume fraction of pores:17 Describe the difference in fracture mechanism between a boron-reinforced aluminum composite and a glass fiber-reinforced epoxy composite.In the boron-aluminum composite, the aluminum matrix is soft and ductile; thus we expect the matrix to fail in a ductile manner. Boron fibers, in contrast, fail in a brittle manner. Both glass fibers and epoxy are brittle; thus the composite as a whole should display little evidence of ductile fracture.18 Compare engineering stress and strain with true stress and strain for the aluminum alloy in Example 6.1 at (a) the maximum load and (b) fracture. The diameter at maximum load is 0.497 in. and at fracture is 0.398 in.19 An advanced engineered ceramic has a Weibull modulus m = 9. The flexural strength is 250 MPa at a probability of failure F = 0.4. What is the level of flexural strength if the probability of failure has to be 0.1?solutionNow, we want to determine the value of for F = 0.1. We know that m = 9 and 0 = 269.4 MPa, so we need to get the value of . We substitute these values into Equation 6-29:20 Seven silicon carbide specimens were tested and the following fracture strengths were obtained: 23, 49, 34, 30, 55, 43, and 40 MPa. Estimate the Weibull modulus for the data by fitting the data to Equation 7-11. Discuss the reliability of the ceramic.21 A crankshaft in a diesel engine fails. Examination of the crankshaft reveals no plastic deformation. The fracture surface is smooth. In addition, several other cracks appear at other locations in the crankshaft. What type of failure mechanism would you expect?SOLUTIONSince the crankshaft is a rotating part, the surface experiences cyclical loading. We should immediately suspect fatigue. The absence of plastic deformation supports our suspicion. Furthermore, the presence of other cracks is consistent with fatigue; the other cracks didnt have time to grow to the size that produced catastrophic failure. Examination of the fracture surface will probably reveal beach marks or fatigue striations.22 A solid shaft for a cement kiln produced from the tool steel in Figure 6.50 must be 96 in. long and must survive continuous operation for one year with an applied load of 12,500 lb. The shaft makes one revolution per minute during operation. Design a shaft that will satisfy these requirements.Solution23 We want to make 1000 kilograms of BaTiO3 ceramic from BaCO3 and TiO2. How much barium carbonate and titanium dioxide should be ball milled and calcined? Even though the actual formation of BaTiO3 involves many different intermediate phases, we can write the final reaction as:BaCO3(s) + TiO2(s) BaTiO3(s) + CO2(g) Molecular weights are: BaCO3: 137(Ba) + 12 (C) + (3 *16(O) = 197 g/mol TiO2: 48(Ti) + (2 *16) = 80 g/mol BaTiO3: 137(Ba) + 48(Ti) + (3 *16(O) = 233 g/mol CO2: 12(C) + 2 *16(O) = 44 g/mol Thus, 197 g of BaCO3 reacts with 80 g of TiO2 to form 233 g of BaTiO3 and 44 g of CO2. Since 233 g of BaTiO3 is produced using 197 g of BaCO3, for 1000 kilograms of BaTiO3, we will need 845.5 kilograms of BaCO3. Similarly, since 233 g of BaTiO3 is produced using 80 grams of TiO2, for 1000 kilograms of BaTiO3, we will need 343.3 kilograms of TiO2.24 Derive the rule of mixtures (Equation 6.5) for the modulus of elasticity of a fiber-reinforced composite when a stress ( ) is applied along the axis of the fibers. We use the symbol for stress to distinguish it from the symbol used for conductivity. The total force acting on the composite is the sum of the forces carried by each constituent: Fc = Fm + Ff Since F = A: If the fibers have a uniform cross-section, the area fraction equals the volume fraction f :From Hookes law, = E. Therefore:If the fibers are rigidly bonded to the matrix, both the fibers and the matrix must stretch equal amounts (iso-strain conditions):25 A manufacturer of barium zinc tantalate (Ba(Zn1/3Ta2/3)O3 or BZT ceramics) produces cylindrical, puck-shaped devices known as dielectric resonators. The particular pucks made in this case are 2 inches in diameter and 1/2 inch tall and they have a 1/2 inch hole at the center. The sintering of these pieces is conducted at 1500oC, using additives. The manufacturing process used to make these pieces is well established. Suddenly, one day, a batch of the dielectric resonators comes out of the furnace with cracks and must be rejected. The plant manager determines that the material has reached 98% of the theoretical target level of densification. What could be the reason for the cracks? Problems such as these have to be traced back through the manufacturing process starting with the raw materials, blending, compaction, and the use of binders. In a quality manufacturing operation (such as the one having a ISO 9000 certification), all raw materials, manufacturing steps, procedures, and suppliers must be traceable. Discussions with th