Question

Tungsten is being used at half its melting point (Tm≈3,400◦C) and astress level of 160 MPa. An engineer suggests increasing the grain size by afactor of 4 as an effective means of reducing the creep rate.(a)Do you agree with the engineer? Why? What if the stress level were equalto 1.6 MPa?(b)What is the predicted increase in length of the specimen after 10,000hours if the initial length is 10 cm?

Answer 1

Increasing the grain size can affect the creep rate of tungsten, particularly at high temperatures, although the effect may change with different stress levels. The increase in length due to creep and thermal expansion requires detailed calculations using specific equations and material properties.

Step-by-step explanation:

The question pertains to the creep behavior of tungsten when operated at half its melting temperature and under a given stress level. The efficiency of grain size increase as a method to reduce creep rate is being evaluated.

(a) Whether increasing the grain size by a factor of 4 would effectively reduce the creep rate depends on the creep mechanism dominant at the given conditions. At high temperatures (close to half the melting point of tungsten), creep is generally controlled by diffusion processes, which can be affected by grain size. A larger grain size would typically reduce the boundary diffusion rate, which can reduce the creep rate. However, if the stress level is reduced to 1.6 MPa, the type of creep and the influence of grain size could change; thus, the effectiveness of increasing grain size in reducing creep rate might also change.

For part (b), to predict the increase in length of a tungsten specimen after 10,000 hours, creep equations and the factors such as temperature, stress, and grain size need to be considered. Additionally, thermal expansion due to the operating temperature will also contribute to the length change.

Due to the complexity of creep behavior and the absence of a specific creep equation or parameters in the provided question, a numerical answer for the length increase cannot be provided here. Creep calculations require detailed material properties and conditions, which must be available to make accurate predictions.

Answer 2

Step-by-step explanation:

The missing diagram is attached in the image below which shows the deformation map of the Tungsten.

Given that:

Stress level
`\sigma = 160 MPa`

T = 0.5 Tm

`\implies (T)/(Tm) = 0.5`

G = 160 GPa

`\implies (\sigma)/(G) = 10^(-3)`

a)

The regulating creep mechanism is dislocation driven, as we can see from the deformation mechanism.

The engineer's recommendation would not be approved because increasing grain size results in a decrease in the grain-boundary count, preferring dislocation motion. The existence of grain borders is a hindrance to dislocation motion, as the dislocation principle explicitly states. To stop the motion, we'll need a substance with finer grains, which would result in more grain borders, or a material with higher pressure. In the case of Nabarro creep, which is diffusion-driven, an engineer's recommendation would be useful.

b)

If stress level reduced to
`\sigma = 1.6 MPa`

`\implies (\sigma )/(G) = 10^(-5)`

Cable creep is now the controlling creep mode, which entails tension-driven atom diffusion along grain borders to elongate grain along the stress axis, a process known as grain-boundary diffusion. Cable creep is more common in fine-grained materials. As a result, the engineer's advice would succeed in this case. The affinity for cable creep is reduced when the grain size is increased.

c)

From the map of creep mechanism for
`(\sigma)/(G) = 10^(-3) \ and \ (T)/(Tm) = 0.5`

We read strain rate
`(e) = 10^(-6)/sec`

Therefore,

`Strain (E) = e * \Delta t`

`= 10^(-6) * 10000 * 3600`

= 36

Therefore,
`\Delta L = E * Li`

=
`36 * 10 cm`

= 360 cm

Thus, the increase in length = 360 cm