A specimen of a 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa/m (50 ksi/in ) is exposed to a stress of 1077 MPa (156200 psi). Assume that the parameter Y has a value of 1.06. If the largest internal crack is 1.8 mm (0.0709 in.) long, Will this specimen experience fracture? Attach File Browse My Computer Browse Content Collection
A specimen of a 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa/m (50 ksi/in ) is exposed to a stress of 1077 MPa (156200 psi). Assume that the parameter Y has a value of 1.06. If the largest internal crack is 1.8 mm (0.0709 in.) long, Will this specimen experience fracture? Attach File Browse My Computer Browse Content Collection
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![**Question 11**
A specimen of a 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa√m (50 ksi√in) is exposed to a stress of 1077 MPa (156200 psi). Assume that the parameter Y has a value of 1.06. If the largest internal crack is 1.8 mm (0.0709 in.) long, will this specimen experience fracture?
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### Analysis
In this problem, we're asked to determine if a steel alloy specimen will experience fracture under given conditions. The key values provided are:
- **Plane Strain Fracture Toughness, K_Ic**: 54.8 MPa√m
- **Stress, σ**: 1077 MPa
- **Parameter Y**: 1.06
- **Crack length, a**: 1.8 mm
### Key Concepts
The critical condition for fracture can be assessed using the following formula:
\[ K_I = Y \cdot \sigma \cdot \sqrt{(\pi \cdot a)} \]
Where:
- \( K_I \) is the stress intensity factor.
- \( Y \) is a dimensionless parameter specific to the geometry.
- \( \sigma \) is the applied stress.
- \( a \) is the crack length.
The specimen will experience fracture if \( K_I \) reaches or exceeds \( K_Ic \).
### Step-by-Step Calculation
1. **Convert the crack length to meters**:
\( a = 1.8 \, \text{mm} = 0.0018 \, \text{m} \)
2. **Calculate \( K_I \) using the given stress and crack length**:
\[
K_I = 1.06 \cdot 1077 \, \text{MPa} \cdot \sqrt{(\pi \cdot 0.0018 \, \text{m})}
\]
3. **Compare \( K_I \) to \( K_Ic \)**:
- If \( K_I \geq 54.8 \, \text{MPa}\sqrt{\text{m}} \), the material will fracture.
### Considerations
Understanding these calculations is crucial for predicting material failures in safety-critical applications such](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54ee9614-c34a-457c-aea7-f186a7974fc7%2F1bb7c5e9-7041-4cc4-a143-9638c16450b4%2Ftsikkj_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 11**
A specimen of a 4340 steel alloy with a plane strain fracture toughness of 54.8 MPa√m (50 ksi√in) is exposed to a stress of 1077 MPa (156200 psi). Assume that the parameter Y has a value of 1.06. If the largest internal crack is 1.8 mm (0.0709 in.) long, will this specimen experience fracture?
*[Attach File]*
*[Browse My Computer]* *[Browse Content Collection]*
---
### Analysis
In this problem, we're asked to determine if a steel alloy specimen will experience fracture under given conditions. The key values provided are:
- **Plane Strain Fracture Toughness, K_Ic**: 54.8 MPa√m
- **Stress, σ**: 1077 MPa
- **Parameter Y**: 1.06
- **Crack length, a**: 1.8 mm
### Key Concepts
The critical condition for fracture can be assessed using the following formula:
\[ K_I = Y \cdot \sigma \cdot \sqrt{(\pi \cdot a)} \]
Where:
- \( K_I \) is the stress intensity factor.
- \( Y \) is a dimensionless parameter specific to the geometry.
- \( \sigma \) is the applied stress.
- \( a \) is the crack length.
The specimen will experience fracture if \( K_I \) reaches or exceeds \( K_Ic \).
### Step-by-Step Calculation
1. **Convert the crack length to meters**:
\( a = 1.8 \, \text{mm} = 0.0018 \, \text{m} \)
2. **Calculate \( K_I \) using the given stress and crack length**:
\[
K_I = 1.06 \cdot 1077 \, \text{MPa} \cdot \sqrt{(\pi \cdot 0.0018 \, \text{m})}
\]
3. **Compare \( K_I \) to \( K_Ic \)**:
- If \( K_I \geq 54.8 \, \text{MPa}\sqrt{\text{m}} \), the material will fracture.
### Considerations
Understanding these calculations is crucial for predicting material failures in safety-critical applications such
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