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Problem 1: A plastic component was subjected to a series of step changes in stress as follows: 1) An initial constant stress of 10 MN/m² was applied for 1000 seconds. 2) Then, the stress level was increased to a constant level of 20 MN/m². 3) After a further 1000 seconds the stress level was decreased to 5 MN/m² which was maintained for 1000 seconds. 4) Then, the stress was increased to 25 MN/m² for 1000 seconds. 5) After that, the stress was completely removed. If the material may be represented by a Kelvin-Voigt model in which the elastic constant E = 1.25 GN/m² and the viscous constant n= 125 GNs/m², calculate the strain 4500 seconds after the first stress was applied.

Problem 1: A plastic component was subjected to a series of step changes in stress as follows: 1) An initial constant stress of 10 MN/m² was applied for 1000 seconds. 2) Then, the stress level was increased to a constant level of 20 MN/m². 3) After a further 1000 seconds the stress level was decreased to 5 MN/m² which was maintained for 1000 seconds. 4) Then, the stress was increased to 25 MN/m² for 1000 seconds. 5) After that, the stress was completely removed. If the material may be represented by a Kelvin-Voigt model in which the elastic constant E = 1.25 GN/m² and the viscous constant n= 125 GNs/m², calculate the strain 4500 seconds after the first stress was applied.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Please solve only problem 3.
Problem 1: A plastic component was subjected to a series of step changes in stress as follows: 1) An initial constant stress of 10 MN/m² was applied for 1000 seconds. 2) Then, the stress level was increased to a constant level of 20 MN/m². 3) After a further 1000 seconds the stress level was decreased to 5 MN/m² which was maintained for 1000 seconds. 4) Then, the stress was increased to 25 MN/m² for 1000 seconds. 5) After that, the stress was completely removed. If the material may be represented by a Kelvin-Voigt model in which the elastic constant E = 1.25 GN/m? and the viscous constant n= 125 GNs/m², calculate the strain 4500 seconds after the first stress was applied. Problem 2: If the stress application of Problem 1 is conducted on another polymer at 45C, estimate the strain 4500 seconds after the first stress was applied. The plastic used, this time, has a glass transition temperature of -20°C. The modulus of elasticity, E(t), of this polymer at room temperature (25°C) was determined to be: E(t) = 1.39 t0.155 GPa Where t is in seconds. Problem 3: The material of Problem 2 is being used as a bolt for joining two rigid plates. The bolt is quickly tightened so that the initial stress is 15.0 MPa. After 48 hours the bolt is retightened to keep the same clamping force. Find the remaining stress value after further one week at 37°C.
Transcribed Image Text:Problem 1: A plastic component was subjected to a series of step changes in stress as follows: 1) An initial constant stress of 10 MN/m² was applied for 1000 seconds. 2) Then, the stress level was increased to a constant level of 20 MN/m². 3) After a further 1000 seconds the stress level was decreased to 5 MN/m² which was maintained for 1000 seconds. 4) Then, the stress was increased to 25 MN/m² for 1000 seconds. 5) After that, the stress was completely removed. If the material may be represented by a Kelvin-Voigt model in which the elastic constant E = 1.25 GN/m? and the viscous constant n= 125 GNs/m², calculate the strain 4500 seconds after the first stress was applied. Problem 2: If the stress application of Problem 1 is conducted on another polymer at 45C, estimate the strain 4500 seconds after the first stress was applied. The plastic used, this time, has a glass transition temperature of -20°C. The modulus of elasticity, E(t), of this polymer at room temperature (25°C) was determined to be: E(t) = 1.39 t0.155 GPa Where t is in seconds. Problem 3: The material of Problem 2 is being used as a bolt for joining two rigid plates. The bolt is quickly tightened so that the initial stress is 15.0 MPa. After 48 hours the bolt is retightened to keep the same clamping force. Find the remaining stress value after further one week at 37°C.
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