Ask question

Ask question

All categories

3 years ago

11

A structural component in the shape of a flat plate 29.6 mm thick is to be fabricated from a metal alloy for which the yield str

ength and plane strain fracture toughness values are 535 MPa and 38.5 MPa-m1/2, respectively. For this particular geometry, the value of Y is 1.5. Assuming a design stress of 0.5 times the yield strength, calculate the critical length of a surface flaw. mm

1 answer:

slega [8]3 years ago

8 0

Answer:

2.93 mm

Explanation:

Plane strain fracture toughness $K_{IC}=38.5 Mpa\sqrt{m}$

Yield strength, $\sigma=535 Mpa$

Design stress=0.5*535=267.5 Mpa

Dimensionless parameter Y=1.5

Critical length of surface flaw is given by

$a_c=\frac {1}{\pi}\times (\frac {K_{IC}}{Y\sigma})^{2}=\frac {1}{\pi}\times (\frac {38.5}{1.5*267.5})^{2}= 0.00293\approx 2.93 mm$

You might be interested in

Please answer fast. With full step by step solution.

lina2011 [118]

Let <em>f(z)</em> = (4<em>z </em>² + 2<em>z</em>) / (2<em>z </em>² - 3<em>z</em> + 1).

First, carry out the division:

<em>f(z)</em> = 2 + (8<em>z</em> - 2) / (2<em>z </em>² - 3<em>z</em> + 1)

Observe that

2<em>z </em>² - 3<em>z</em> + 1 = (2<em>z</em> - 1) (<em>z</em> - 1)

so you can separate the rational part of <em>f(z)</em> into partial fractions. We have

(8<em>z</em> - 2) / (2<em>z </em>² - 3<em>z</em> + 1) = <em>a</em> / (2<em>z</em> - 1) + <em>b</em> / (<em>z</em> - 1)

8<em>z</em> - 2 = <em>a</em> (<em>z</em> - 1) + <em>b</em> (2<em>z</em> - 1)

8<em>z</em> - 2 = (<em>a</em> + 2<em>b</em>) <em>z</em> - (<em>a</em> + <em>b</em>)

so that <em>a</em> + 2<em>b</em> = 8 and <em>a</em> + <em>b</em> = 2, yielding <em>a</em> = -4 and <em>b</em> = 6.

So we have

<em>f(z)</em> = 2 - 4 / (2<em>z</em> - 1) + 6 / (<em>z</em> - 1)

or

<em>f(z)</em> = 2 - (2/<em>z</em>) (1 / (1 - 1/(2<em>z</em>))) + (6/<em>z</em>) (1 / (1 - 1/<em>z</em>))

Recall that for |<em>z</em>| < 1, we have

$\displaystyle\frac1{1-z}=\sum_{n=0}^\infty z^n$

Replace <em>z</em> with 1/<em>z</em> to get

$\displaystyle\frac1{1-\frac1z}=\sum_{n=0}^\infty z^{-n}$

so that by substitution, we can write

$\displaystyle f(z) = 2 - \frac2z \sum_{n=0}^\infty (2z)^{-n} + \frac6z \sum_{n=0}^\infty z^{-n}$

Now condense <em>f(z)</em> into one series:

$\displaystyle f(z) = 2 - \sum_{n=0}^\infty 2^{-n+1} z^{-(n+1)} + 6 \sum_{n=0}^\infty z^{-n-1}$

$\displaystyle f(z) = 2 - \sum_{n=0}^\infty \left(6+2^{-n+1}\right) z^{-(n+1)}$

$\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{-(n-1)+1}\right) z^{-n}$

$\displaystyle f(z) = 2 - \sum_{n=1}^\infty \left(6+2^{2-n}\right) z^{-n}$

So, the inverse <em>Z</em> transform of <em>f(z)</em> is $\boxed{6+2^{2-n}}$ .

4 0

3 years ago

How old are legos? Who created them? Why did they create them?

Sunny_sXe [5.5K]

“How old are the legos” 89 years old.

“Who created them?” Ole Kirk Christiansen.

“Why did they created them?” As a you man, Christiansen turned his love of whittling and playing with wood into a Business and, in 1916, he opened his own shop. Since times were so hard, Christiansen made the hard decision to use his wood to create inexpensive goods that might actually sell. Among them were Cheap toys.

Hope this helps•

Bye~

•Kate•

4 0

3 years ago

What are the three elementary parts of a vibrating system?

zhenek [66]

Answer:

the three part are mass, spring, damping

Explanation:

vibrating system consist of three elementary system namely

1) Mass - it is a rigid body due to which system experience vibration and kinetic energy due to vibration is directly proportional to velocity of the body.

2) Spring - the part that has elasticity and help to hold mass

3) Damping - this part considered to have zero mass and zero elasticity.

7 0

3 years ago

What do we need to do to get CO2 emissions all the way to zero?

Svetlanka [38]

Answer:

A key element is powering economies with clean energy, replacing polluting coal - and gas and oil-fired power stations - with renewable energy sources, such as wind or solar farms. This would dramatically reduce carbon emissions. Plus, renewable energy is now not only cleaner, but often cheaper than fossil fuels

Explanation:

here is your answer if you like my answer please follow

3 0

3 years ago

If a heat engine has an efficiency of 30% and its power output is 600 W, what is the rate of heat input from the combustion phas

jarptica [38.1K]

Answer:

The heat input from the combustion phase is 2000 watts.

Explanation:

The energy efficiency of the heat engine ( $\eta$ ), no unit, is defined by this formula:

$\eta = \frac{\dot W}{\dot Q}$ (1)

Where:

$\dot Q$ - Heat input, in watts.

$\dot W$ - Power output, in watts.

If we know that $\dot W = 600\,W$ and $\eta = 0.3$ , then the heat input from the combustion phase is:

$\eta = \frac{\dot W}{\dot Q}$

$\dot Q = \frac{\dot W}{\eta}$

$\dot Q = \frac{600\,W}{0.3}$

$\dot Q = 2000\,W$

The heat input from the combustion phase is 2000 watts.

8 0

3 years ago