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Inessa05 [86]
3 years ago
14

A tensile test is performed on a metal specimen, and it is found that a true plastic strain of 0.20 is produced when a true stre

ss of 578 MPa (83830 psi) is applied; for the same metal, the value of K in the equation is 860 MPa (124700 psi).
Calculate the true strain that results from the application of a true stress of 600 MPa (87020 psi).
Engineering
2 answers:
Tanya [424]3 years ago
8 0

Answer:

The true strain that results from the application of a true stress of 600 MPa, will be 1.25.

Explanation:

The relation between true stress and true strain is given by the following formula:

σ = K (ε)^n

First, we find the value of n by substituting the values found by first test:

σ = 578 MPa

K = 860 MPa

ε = 0.2

Therefore,

578 MPa = (860 MPa)(0.2)^n

0.2^n = 0.67209

taking ln on both sides:

n ln(0.2) = ln(0.67209)

n = -0.3973/ln(0.2)

n = -1.6

Now, for the new stress value of 600 MPa, we calculate the strain:

600 MPa = (860 MPa)(ε)^-1.6

(ε)^1.6 = 1.4333

Taking power 1/1.6 on both sides, we get:

<u>ε = 1.25</u>

disa [49]3 years ago
6 0

Answer:

0.234

Explanation:

True stress is ratio of instantaneous load acting on instantaneous cross-sectional area

σ = k × (ε)^n  

σ = true stress

ε = true strain

k = strength coefficient

n = strain hardening exponent

ε = ( σ / k) ^1/n

take log of both side

log ε = \frac{1}{n} ( log σ  - log k)

n = ( log σ  - log k) / log ε

n = (log 578 - log 860) / log 0.20 = 0.247

the new ε = ( 600 / 860)^( 1 / 0.247) = 0.234

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What are the four categories of engineering materials used in manufacturing?
alexgriva [62]

Answer:

metals, composite, ceramics and polymers.

Explanation:

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8 0
3 years ago
A large plate is fabricated from a steel alloy that has a plane strain fracture toughness of 55 MPa √m (50 ksi √in.). If, during
astra-53 [7]

Answer:

0.024 m = 24.07 mm

Explanation:

1) Notation

\sigma_c = tensile stress = 200 Mpa

K = plane strain fracture toughness= 55 Mpa\sqrt{m}

\lambda= length of a surface crack (Variable of interest)

2) Definition and Formulas

The Tensile strength is the ability of a material to withstand a pulling force. It is customarily measured in units (F/A), like the pressure. Is an important concept in engineering, especially in the fields of materials and structural engineering.

By definition we have the following formula for the tensile stress:

\sigma_c=\frac{K}{Y\sqrt{\pi\lambda}}   (1)

We are interested on the minimum length of a surface that will lead to a fracture, so we need to solve for \lambda

Multiplying both sides of equation (1) by Y\sqrt{\pi\lambda}

\sigma_c Y\sqrt{\pi\lambda}=K   (2)

Sequaring both sides of equation (2):

(\sigma_c Y\sqrt{\pi\lambda})^2=(K)^2  

\sigma^2_c Y^2 \pi\lambda=K^2   (3)

Dividing both sides by \sigma^2_c Y^2 \pi we got:

\lambda=\frac{1}{\pi}[\frac{K}{Y\sigma_c}]^2   (4)

Replacing the values into equation (4) we got:

\lambda=\frac{1}{\pi}[\frac{55 Mpa\sqrt{m}}{1.0(200Mpa)}]^2 =0.02407m

3) Final solution

So the minimum length of a surface crack that will lead to fracture, would be 24.07 mm or more.

7 0
3 years ago
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