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Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120?
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Three fracture toughness samples of an aluminum alloy have identical E...
Fracture Toughness Calculation for Aluminum Alloy
To calculate the fracture toughness of the aluminum alloy in plane strain condition, we need to use the formula:
Kic = (Y * σ * sqrt(π * a)) / (E * sqrt(1 - ν^2))
Where:
Kic - Fracture toughness (in MN/m^3)
Y - Correction factor
σ - Applied stress (in Pa)
a - Crack length (in m)
E - Young's modulus of the material (in Pa)
ν - Poisson's ratio of the material
Step 1: Calculation of Crack Length
The crack length can be calculated using the formula:
a = (ΔL * L0) / ΔL0
Where:
a - Crack length (in m)
ΔL - Elongation in the gauge length (in mm)
L0 - Original gauge length (in mm)
For the given data, the crack lengths are as follows:
Sample 1: a = (0.26 * 219.5) / 120 = 0.47475 mm
Sample 2: a = (0.263 * 219.5) / 185 = 0.31118 mm
Sample 3: a = (0.263 * 219.5) / 120 = 0.48032 mm
Step 2: Calculation of Applied Stress
The applied stress can be calculated using the formula:
σ = P / (b * h)
Where:
σ - Applied stress (in Pa)
P - Load applied (in N)
b - Width of the sample (in m)
h - Thickness of the sample (in m)
Since the external dimensions and thickness of all samples are identical, the applied stress will be the same for all samples.
Step 3: Calculation of Fracture Toughness
Using the calculated crack lengths and the applied stress, we can now calculate the fracture toughness using the given values of Young's modulus and Poisson's ratio.
Kic = (Y * σ * sqrt(π * a)) / (E * sqrt(1 - ν^2))
Substituting the values:
E = 70 GN/m^2 = 70 × 10^9 N/m^2
ν = 0.3
For the given data, the fracture toughness of the aluminum alloy in plane strain condition (Kic) can be calculated as follows:
Sample 1: Kic = (Y * σ * sqrt(π * 0.47475 * 10^-3)) / (70 × 10^9 * sqrt(1 - 0.3^2))
Sample 2: Kic = (Y * σ * sqrt(π * 0.31118 * 10^-3)) / (70 × 10^9 * sqrt(1 - 0.3^2))
Sample 3: Kic = (Y * σ * sqrt(π * 0.48032 * 10^-3)) / (70 × 10^9 * sqrt(1 - 0.3^2))
Note: The correction factor Y depends on the geometry and loading conditions of the sample, which is not provided in the given data. Therefore, the exact values of fracture toughness cannot be calculated without the correction factor.
To calculate the fracture toughness of the aluminum alloy in plane strain condition, we need to use the formula:
Kic = (Y * σ * sqrt(π * a)) / (E * sqrt(1 - ν^2))
Where:
Kic - Fracture toughness (in MN/m^3)
Y - Correction factor
σ - Applied stress (in Pa)
a - Crack length (in m)
E - Young's modulus of the material (in Pa)
ν - Poisson's ratio of the material
Step 1: Calculation of Crack Length
The crack length can be calculated using the formula:
a = (ΔL * L0) / ΔL0
Where:
a - Crack length (in m)
ΔL - Elongation in the gauge length (in mm)
L0 - Original gauge length (in mm)
For the given data, the crack lengths are as follows:
Sample 1: a = (0.26 * 219.5) / 120 = 0.47475 mm
Sample 2: a = (0.263 * 219.5) / 185 = 0.31118 mm
Sample 3: a = (0.263 * 219.5) / 120 = 0.48032 mm
Step 2: Calculation of Applied Stress
The applied stress can be calculated using the formula:
σ = P / (b * h)
Where:
σ - Applied stress (in Pa)
P - Load applied (in N)
b - Width of the sample (in m)
h - Thickness of the sample (in m)
Since the external dimensions and thickness of all samples are identical, the applied stress will be the same for all samples.
Step 3: Calculation of Fracture Toughness
Using the calculated crack lengths and the applied stress, we can now calculate the fracture toughness using the given values of Young's modulus and Poisson's ratio.
Kic = (Y * σ * sqrt(π * a)) / (E * sqrt(1 - ν^2))
Substituting the values:
E = 70 GN/m^2 = 70 × 10^9 N/m^2
ν = 0.3
For the given data, the fracture toughness of the aluminum alloy in plane strain condition (Kic) can be calculated as follows:
Sample 1: Kic = (Y * σ * sqrt(π * 0.47475 * 10^-3)) / (70 × 10^9 * sqrt(1 - 0.3^2))
Sample 2: Kic = (Y * σ * sqrt(π * 0.31118 * 10^-3)) / (70 × 10^9 * sqrt(1 - 0.3^2))
Sample 3: Kic = (Y * σ * sqrt(π * 0.48032 * 10^-3)) / (70 × 10^9 * sqrt(1 - 0.3^2))
Note: The correction factor Y depends on the geometry and loading conditions of the sample, which is not provided in the given data. Therefore, the exact values of fracture toughness cannot be calculated without the correction factor.
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Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120?
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Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120?.
Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three fracture toughness samples of an aluminum alloy have identical External dimensions and a thickness of 25 mm. If the Young's modulus and Poisson's ratio values for the aluminum are 70 GN/m2 and 0.3 respectively, calculate the Fracture toughness of the material in plane strain condition (Kic in MN/m3) Test Sample Crack Load applied (kN) |Sample Length(mm) Elongation in 219.5 mm 120 0.26 1 20 Sample Fractured 0.263 185 3 20.5 120?.
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