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Ratling [72]
3 years ago
9

A crystalline grain of aluminum in a metal plate is situated so that a tensile load is oriented along the [1 1 1] direction. Wha

t tensile stress is required (to 3 significant figures) to produce a critical resolved shear stress of 0.242 MPa along [1 0 1] in the (1 1 -1) plane
Engineering
1 answer:
Ivenika [448]3 years ago
3 0

Answer: required tensile stress is 0.889 MPa

Explanation:

Given that;

tensile load is oriented along the [1 1 1] direction

shear stress is 0.242 MPa along [1 0 1] in the (1 1 -1) plane

first we determine

λ which is Angle between  [1 1 1]  and  [1 0 1]

so

cosλ = [ 1(1) +  1(0) + 1(1) ] / [ √(1² + 1² + 1²) √(1² + 0² + 1²)]

= 2 / √3√2 =  2/√6

Next, we determine ∅ which is angle between [1 1 1]  and  [1 1 -1]

so,

cos∅ = [ 1(1) +  1(1) + 1(-1) ] / [ √(1² + 1² + 1²) √(1² + 1² + (-1)²)]

cos∅ = [ 2-1] / [√3√3 ]

cos∅ = 1/3

Now, we know that;

σ = T_stress/cosλcosθ

so we substitute

σ = 0.242 / ( 2/√6 × 1/3 )

σ = 0.242 / 0.2721

σ = 0.889 MPa

Therefore, required tensile stress is 0.889 MPa

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Answer:

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Explanation:

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Then, we should apply the values in the COP.

                           =\frac{1.15\;T_L}{1.15-1}

                           =7.67

The number of heat rejected by the heat pump must then be calculated.

                   Q_H=COP_{HP}\times W_{nst}

                          =7.67\times5=38.35

We must then calculate the refrigerant mass flow rate.

                   m=0.264\;kg/s

                   q_H=\frac{Q_H}{m}

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The pressure at 64 ° C is thus 1849.36 kPa by interpolation.

And, the lowest reservoir temperature must be calculated.

                   T_L=\frac{T_H}{1.15}

                        =\frac{64+273}{1.15}=293.04

                        =19.89\°C

the lowest reservoir temperature = 258.703  kpa                    

So, the pressure ratio should be = 7.15

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