
Concept explainers
(a)
The strain where the first change in elastic modulus occurs in composite material.
(a)

Answer to Problem 12.12P
Matrix will rupture before the fiber at the strain of
Explanation of Solution
Given:
Elastic modulus of Boronis
Tensile strength of Boronis
Elastic modulus of Aluminumis
Yield strength of Aluminumis
Ultimate tensile strength of aluminum is
Concept used:
Write the expression for failure strain in Fiber.
Here,
Write the expression for failure strain in Matrix.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, matrix will rupture before the fiber at the strain of
(b)
The composite stress where the change in elastic modulus occurs.
(b)

Answer to Problem 12.12P
The composite stress where the change in elastic modulus occurs is
Explanation of Solution
Given:
Volume percent of Boron fiber is
Volume percent of Aluminumis
Strain at fracture of Aluminumis
Concept used:
Write the expression for stress carried by composite.
Here,
Write the expression for stress in fiber by considering the iso-strain model for axial strain.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the composite stress where the change in elastic modulus occurs is
(c)
The elastic modulus at low strain and the elastic modulus after Aluminum yields, if Aluminum yields before fiber fails.
(c)

Answer to Problem 12.12P
The elastic modulus at low strain is
Explanation of Solution
Concept used:
Write the expression for modulus of elasticity of composite.
Here,
Calculation:
Substitute
After yielding of matrix the elastic modulus of composite is the elastic modulus of fiber in it. Therefore, the elastic modulus will be equal to 60% of
Conclusion:
Thus, the elastic modulus at low strain is
(d)
Fracture strength of composite.
(d)

Answer to Problem 12.12P
Fracture strength of composite is
Explanation of Solution
Concept used:
Write the expression for fracture strength.
Here,
Calculation:
Substitute
Conclusion:
Thus, the Fracture strength of composite is
Want to see more full solutions like this?
Chapter 12 Solutions
Materials Science And Engineering Properties
- Show step by step solutionarrow_forwardDraw the shear and the moment diagrams for each of the frames below. If the frame is statically indeterminate the reactions have been provided. Problem 1 (Assume pin connections at A, B and C). 30 kN 2 m 5 m 30 kN/m B 60 kN 2 m 2 m A 22 CO Carrow_forwardThis is an old exam practice question. The answer key says the answer is Pmax = 52.8kN but I am confused how they got that.arrow_forward
- F12-45. Car A is traveling with a constant speed of 80 km/h due north, while car B is traveling with a constant speed of 100 km/h due east. Determine the velocity of car B relative to car A. pload Choose a File Question 5 VA - WB VBA V100 111413 + *12-164. The car travels along the circular curve of radius r = 100 ft with a constant speed of v = 30 ft/s. Determine the angular rate of rotation è of the radial liner and the magnitude of the car's acceleration. Probs. 12-163/164 pload Choose a File r = 400 ft 20 ptsarrow_forwardPlease show step by step how to solve this and show formulararrow_forwardPlease solve this question step by step with dia gramarrow_forward
- Use the second picture to answer the question, Thank you so much for your help!arrow_forwardP6.16 A compound shaft (Figure P6.16) consists of a titanium alloy [G= 6,200 ksi] tube (1) and a solid stainless steel [G= 11,500 ksi] shaft (2). Tube (1) has a length L₁ = 40 in., an outside diameter D₁ = 1.75 in., and a wall thickness t₁ = 0.125 in. Shaft (2) has a length 42 = 50 in. and a diameter d₂ = 1.25 in. If an external torque TB = 580 lb ft acts at pulley B in the direction shown, calculate the torque Tcrequired at pulley C so that the rotation angle of pulley Crelative to A is zero. B Te (2) TB (1) FIGURE P6.16arrow_forward7.43 Neglecting head losses, determine what horsepower the pump must deliver to produce the flow as shown. Here, the elevations at points A, B, C, and D are 124 ft, 161 ft, 110 ft, and 90 ft, respectively. The nozzle area is 0.10 ft². B Nozzle Water C Problem 7.43arrow_forward
- A 1.8m x 1.8m footing is located at a depth of 1 m below the ground surface in a deep deposit of compacted sand (f'= 33 , f' = 28 , γ = 17.5 kN/m). Calculate the ultimate net bearing capacity considering several factors (e.g., shape, depth, and inclination) when the groundwater table is located (a) at 5 m below the footing base, (b) at the ground surface, (c) at the footing base, and (d) at 1.5 m below the footing base. Also, explain the effects of the groundwater levels in the bearing capacities of the footing with your own words. If the information is not given for the calculation, please assume it reasonably.arrow_forward7.18 Determine the discharge in the pipe and the pressure at point B. Neglect head losses. Assume α = 1.0 at all locations. 1.5 m Water B 3.5 m 40 cm diameter -20 cm diameter nozzle Problem 7.18arrow_forwardA 200-lb block is at rest on a 30° inclined plane. The coefficient of friction between the block and the inclined plane is 0.20. Compute the value of a horizontal force P that will cause motion to impend the block up the inclined plane. 200 lb P 30°arrow_forward
- Materials Science And Engineering PropertiesCivil EngineeringISBN:9781111988609Author:Charles GilmorePublisher:Cengage Learning
