Page 1 Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input The Lecture Contains: Laminated beam subjected to mechanical input Numerical analysis for MS composites Symmetric laminate with MS layer at the mid plane Symmetric laminate with MS layer at mid plane subjected to mechanical input Symmetric laminate with MS layer away from mid plane file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM] Page 2 Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input The Lecture Contains: Laminated beam subjected to mechanical input Numerical analysis for MS composites Symmetric laminate with MS layer at the mid plane Symmetric laminate with MS layer at mid plane subjected to mechanical input Symmetric laminate with MS layer away from mid plane file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Laminated beam subjected to mechanical input A mechanical force of the form of is assumed to be acting on the beam. Assuming mid plane strain and curvature as and t Strain in the MS layer Corresponding stress in the MS layer (32.1) Hence, the voltage response can be obtained as (32.2) With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory. file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM] Page 3 Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input The Lecture Contains: Laminated beam subjected to mechanical input Numerical analysis for MS composites Symmetric laminate with MS layer at the mid plane Symmetric laminate with MS layer at mid plane subjected to mechanical input Symmetric laminate with MS layer away from mid plane file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Laminated beam subjected to mechanical input A mechanical force of the form of is assumed to be acting on the beam. Assuming mid plane strain and curvature as and t Strain in the MS layer Corresponding stress in the MS layer (32.1) Hence, the voltage response can be obtained as (32.2) With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory. file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Numerical analysis for MS composites Using the basis presented in the previous section, voltage output in magnetostrictive sensory layer has been numerically determined using symmetric as well as asymmetric laminates. The effect of mechanical input along with magnetostriction is also presented taking both symmetric and asymmetric laminate configurations. Numerical inputs used in the analysis are presented in Table 32.1 Table.32.1. Numerical details used in the analysis Composite carbon - epoxy Symmetric laminate stacking [0/90/0/45/m/45/0/90/0] Asymmetric laminate stacking [0/90/0/45/0/90/m/90/0] [45/-45/0/0/90/90/0/0/-45/m/45] Thickness of the composite lamina 0.4 mm Thickness of the MS layer 0.4 mm Elastic modulus of the carbon fiber 350 GPa Elastic modulus of the epoxy matrix 3.50 GPa Elastic modulus of Terfenol-D 30 GPa Volume fraction of the fiber 0.16 Volume fraction of Terfenol-D 0.0224 Poisson's ratio of the carbon fiber 0.3 Poisson's ratio of the epoxy matrix 0.4 Poisson's ratio for Terfenol-D 0.25 Number of turns in the coil per meter 1000 Carrier frequency,? 1000 Hz Carrier current 0.4 A Piezo-magnetic coefficient, d 1.5 e -8 m/A Permeability, µ 14.13e -7 Coupling coefficient of Terfenol-D, k 0.75 Tensile strength of Terfenol-D 28 MPa Compressive strength of Terfenol-D 700 MPa Fracture toughness of MS layer 30 MPa-m 1/2 Size of crack at delamination, c 2 mm Length of beam, l 100 mm Width of beam, b 20 mm file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_3.html [4/4/2013 3:57:09 PM] Page 4 Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input The Lecture Contains: Laminated beam subjected to mechanical input Numerical analysis for MS composites Symmetric laminate with MS layer at the mid plane Symmetric laminate with MS layer at mid plane subjected to mechanical input Symmetric laminate with MS layer away from mid plane file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Laminated beam subjected to mechanical input A mechanical force of the form of is assumed to be acting on the beam. Assuming mid plane strain and curvature as and t Strain in the MS layer Corresponding stress in the MS layer (32.1) Hence, the voltage response can be obtained as (32.2) With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory. file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Numerical analysis for MS composites Using the basis presented in the previous section, voltage output in magnetostrictive sensory layer has been numerically determined using symmetric as well as asymmetric laminates. The effect of mechanical input along with magnetostriction is also presented taking both symmetric and asymmetric laminate configurations. Numerical inputs used in the analysis are presented in Table 32.1 Table.32.1. Numerical details used in the analysis Composite carbon - epoxy Symmetric laminate stacking [0/90/0/45/m/45/0/90/0] Asymmetric laminate stacking [0/90/0/45/0/90/m/90/0] [45/-45/0/0/90/90/0/0/-45/m/45] Thickness of the composite lamina 0.4 mm Thickness of the MS layer 0.4 mm Elastic modulus of the carbon fiber 350 GPa Elastic modulus of the epoxy matrix 3.50 GPa Elastic modulus of Terfenol-D 30 GPa Volume fraction of the fiber 0.16 Volume fraction of Terfenol-D 0.0224 Poisson's ratio of the carbon fiber 0.3 Poisson's ratio of the epoxy matrix 0.4 Poisson's ratio for Terfenol-D 0.25 Number of turns in the coil per meter 1000 Carrier frequency,? 1000 Hz Carrier current 0.4 A Piezo-magnetic coefficient, d 1.5 e -8 m/A Permeability, µ 14.13e -7 Coupling coefficient of Terfenol-D, k 0.75 Tensile strength of Terfenol-D 28 MPa Compressive strength of Terfenol-D 700 MPa Fracture toughness of MS layer 30 MPa-m 1/2 Size of crack at delamination, c 2 mm Length of beam, l 100 mm Width of beam, b 20 mm file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_3.html [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Symmetric laminate with MS layer at the mid plane In the first case, a nine layer symmetric laminate beam [0/90/0/45/m/45/0/90/0] with MS layer in the middle is subjected to actuating current causing magnetostriction to develop in the MS layer leading to compression in it and equivalent balancing stresses in other layers. With increase in magnetostriction by increasing the current rating, the stress and strain level at various interfaces will increase. Variation of stress and strain at various interfaces including the MS layer and voltage induced in MS layer at the time of delamination are shown in Figures 32.1, 32.2 and 32.3. Figure 32.1 Stress variations at various interfaces and in MS layer at the time of delamination when the laminate is subjected to only actuator current file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_4.html (1 of 3) [4/4/2013 3:57:10 PM] Page 5 Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input The Lecture Contains: Laminated beam subjected to mechanical input Numerical analysis for MS composites Symmetric laminate with MS layer at the mid plane Symmetric laminate with MS layer at mid plane subjected to mechanical input Symmetric laminate with MS layer away from mid plane file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Laminated beam subjected to mechanical input A mechanical force of the form of is assumed to be acting on the beam. Assuming mid plane strain and curvature as and t Strain in the MS layer Corresponding stress in the MS layer (32.1) Hence, the voltage response can be obtained as (32.2) With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory. file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Numerical analysis for MS composites Using the basis presented in the previous section, voltage output in magnetostrictive sensory layer has been numerically determined using symmetric as well as asymmetric laminates. The effect of mechanical input along with magnetostriction is also presented taking both symmetric and asymmetric laminate configurations. Numerical inputs used in the analysis are presented in Table 32.1 Table.32.1. Numerical details used in the analysis Composite carbon - epoxy Symmetric laminate stacking [0/90/0/45/m/45/0/90/0] Asymmetric laminate stacking [0/90/0/45/0/90/m/90/0] [45/-45/0/0/90/90/0/0/-45/m/45] Thickness of the composite lamina 0.4 mm Thickness of the MS layer 0.4 mm Elastic modulus of the carbon fiber 350 GPa Elastic modulus of the epoxy matrix 3.50 GPa Elastic modulus of Terfenol-D 30 GPa Volume fraction of the fiber 0.16 Volume fraction of Terfenol-D 0.0224 Poisson's ratio of the carbon fiber 0.3 Poisson's ratio of the epoxy matrix 0.4 Poisson's ratio for Terfenol-D 0.25 Number of turns in the coil per meter 1000 Carrier frequency,? 1000 Hz Carrier current 0.4 A Piezo-magnetic coefficient, d 1.5 e -8 m/A Permeability, µ 14.13e -7 Coupling coefficient of Terfenol-D, k 0.75 Tensile strength of Terfenol-D 28 MPa Compressive strength of Terfenol-D 700 MPa Fracture toughness of MS layer 30 MPa-m 1/2 Size of crack at delamination, c 2 mm Length of beam, l 100 mm Width of beam, b 20 mm file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_3.html [4/4/2013 3:57:09 PM] Objectives_template Module 4: Active SHM using Magnetostrictive Material Lecture 32: Laminated beam subjected to mechanical input Symmetric laminate with MS layer at the mid plane In the first case, a nine layer symmetric laminate beam [0/90/0/45/m/45/0/90/0] with MS layer in the middle is subjected to actuating current causing magnetostriction to develop in the MS layer leading to compression in it and equivalent balancing stresses in other layers. With increase in magnetostriction by increasing the current rating, the stress and strain level at various interfaces will increase. Variation of stress and strain at various interfaces including the MS layer and voltage induced in MS layer at the time of delamination are shown in Figures 32.1, 32.2 and 32.3. Figure 32.1 Stress variations at various interfaces and in MS layer at the time of delamination when the laminate is subjected to only actuator current file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_4.html (1 of 3) [4/4/2013 3:57:10 PM] Objectives_template Figure 32.2 Stress variations at various interfaces and in MS layer at the time of delamination when the laminate is subjected to only actuator current Figure 32.3 Open circuit voltage in MS layer at the time of delamination when the laminate is subjected to only actuator current file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_4.html (2 of 3) [4/4/2013 3:57:10 PM]Read More

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