Hero 10

3) The strength of a titanium piece is found to be 65,000 psi when the grain size is 17 x10-6 m and 82,000 psi when the grain size is 0.8 x10 m. What would be the 9- (a) Constants in the Hall-Petch equation Strength of this titanium piece when the grain size is reduced to 0.2 x10 m. (9)

The yield strength for an alloy that has an average grain diameter of 4.1 × 10-2 mm is 131 MPa. At a grain diameter of 7.6 × 10-3 mm, the yield strength increases to 246 MPa. At what grain diameter, in mm, will the yield strength be 236 MPa?

The yield strength for an alloy that has an average grain diameter of 1.6 × 10-2 mm is 320 MPa. At a grain diameter 3.9 × 10-3³ mm, the yield strength increases to 480 MPa. At what grain diameter (in mm) will the yield strength be 441 MPa? i mm

An uncold-worked brass specimen of average grain size 0.006 mm has a yield strength of 178 MPa. Estimate the yield strength of this alloy (in MPa) after it has been heated to 600°C for 1000 s, if it is known that the value of ky is 11 MPa-mm1/2. The Animated Figure 7.25 may be helpful. Attached is the question and the figure referenced.

Consider a single crystal of some hypothetical metal that has the FCC crystal structure and is oriented such that a tensile stress is applied along a [11 2] direction. If slip occurs on a ( 111) plane and in a [0 11] direction, and the crystal yields at a stress of 5.12 MPa, compute the critical resolved shear stress. CRITICAL RESOLVED SHEAR STRESS • CRITICAL RESOLVED SHEAR STRESS (T, THE MOST FAVORABLY ORIENTED SLIP SYSTEM WHEN SHEAR STRESS IS AT J: SLIP IN A SYSTEM STARTS ON CRSS THIS CRITICAL VALUE • MINIMUM SHEAR STRESS REQUIRED TO INITIATE SLIP • SINGLE CRYSTAL PLASTICALLY DEFORMS WHEN: T, > T, CRSS OR TR(max) =T CRSS 'R Tcrss (cos o cos A)max

Define annealing. (a) What effects does it have on the microstructure? (b) How does this affect dislocation movement? (c) Why/how does this affect the properties?

Consider a single crystal of BCC iron oriented such that tensile stress is applied along a[010] direction. Compute the resolved shear stress along a (110) plane and in a [1⃑ 1 1]direction when a tensile stress of 50 MPa is applied. If Slip occurs on a (110) plane and ina [1⃑ 1 1] direction and the critical resolved shear stress is 25 MPa, calculate themagnitude of the applied tensile stress necessary to initiate yielding.

A hypothetical metal alloy has a grain diameter of 2.4 × 10-2 mm. After a heat treatment at 575°C for 500 min, the grain diameter has increased to 5.6 × 10-2 mm. Compute the time required for a specimen of this same material (i.e., do = 2.4 × 10-² mm) to achieve a grain diameter of 5.5 x 10-2 mm while being heated at 575°C. Assume the n grain diameter exponent has a value of 2.2. i min

A hypothetical metal alloy has a grain diameter of 2.4 x 10-2 mm. After a heat treatment at 575°C for 500 min, the grain diameter has increased to 8.1× 10-2 mm. Compute the time required for a specimen of this same material (i.e., do = 2.4 × 10-2 mm) to achieve a grain diameter of 5.5 × 10-2 mm while being heated at 575°C. Assume the n grain diameter exponent has a value of 2.2.

(6) For an aluminum alloy under constant load, the creep rate increased by a factor of 2 when the temperature was increased from 71°C to 77°C. Find the activation energy and express it in Joule/mole.

A solid solution alloy of Cu containing 10% Ni has a yield strength of 200 MPa. What would you expect the strength of an alloy with 40% Ni to be? Justify answer.

Question The yield strength for an aluminum alloy that has an average grain diameter of 10 um is 400 MPa. As the grain diameter is increased to 80 um, the yield strength decreases to 260 MPa. When the grain diameter is 2 um, its yield strength is close to 760 MPa 668 MPa 566 MPa 419 MPa

Pravinbhai

The flow stress of a coarse-grained dilute copper alloy increased from 2 to 55 MPa when the dislocation density was increased from a low value of 10 cm via cold working to a modest value of 100 cm2. Calculate the flow stress for this alloy when heavy cold working introduces a dislocation density of 10¹2 cm². An equation similar to the Hall-Petch equation has been proposed for dislocations, and is: Tflow To ka Paisl where Tflow is the flow stress (i.e., the force per unit area necessary to get plastic deformation), pdisi is the dislocation density (the dislocation line length per unit volume), and To and ka are constants for a given material. The easiest way to solve this problem is to put values into this equation twice, subtract one expression from the other, and solve for ka. Then enter your value of ka into either original equation to determine To. Keep track of units, and then solve the problem stated above.

Calculate the dislocation spacing of a low-angle tilt boundary in aluminumfor θ = 0.5◦. Take G = 26.1 GPa, v = 0.345, and rAl = 0.143 nm.

When a cold-worked metal is heat-treated below its melting point over a period of time, which of the following phenomena occur? (This question has more than one correct answer) a. Strength is increased b. Dislocation density decreases c. Grain size increases d. Internal lattice strains decrease e. Ductility is reduced

In class I mentioned that an FCC metal should be strongest in uniaxial tension when pulledalong a <111> type direction. Assuming only the preferred {111}/<110> slip systems can beactivated, use the Schmid factor ( cosφ cosλ ) to compare strength in tension along the [100],[211], and [111] directions in an FCC metal. For your final answer, complete the statement,"An FCC metal will be ___% and ___% stronger under tension in the [111] direction comparedto the [100] and [211] directions, respectively.

I am having trouble finding the miller indices for this problem, help would be appreciated. I attempted to find them but was unsure how to find where some of the axes intercepted.

If a series of dislocations produced by a single FrankRead source encounter an impassible barrier, a back stress is created. What is the reason for this back stress, and why is it very effective for dislocations produced by a single F-R source?

4. Johnston and Gilman reported that in a grown LiF crystal that has been subjected to a constantstress of 10.8 MPa, the dislocation velocity at 249.1 K was 6×10-3 cm/s and at 227.3 K thevelocity was 10-6 cm/s. They also observed that their data suggested an Arrhenius relationshipbetween the dislocation velocity and the absolute temperature so that we can write? = ?exp ( ― ?/??)where v is the dislocation velocity, A is a constant of proportionality, Q an effective activationenergy in J/mol, and R is the universal gas constant (8.314 J/mol.K). Determine Q and A usingthe given data and the above equation.  5. A typical cross-head speed in a tensile testing machine is 0.2 in./min. (a) What is thenominal/engineering strain rate imposed by this cross-head speed on a typical engineering tensilespecimen with a 2 inch gauge length? (b) Estimate the average dislocation velocity that would be obtained at this strain rate in analpha-iron specimen with a total dislocation density of 1010 cm-2 of…

Consider an aluminum polycrystal with a grain size of 10 μm. If a dislocationsource at the center of a grain emits dislocations under an appliedshear stress of 50 MPa that pile up at the grain boundaries, what is the stressexperienced by a grain boundary? Take G = 26 GPa and b = 0.3 nm.

Please answer the whole solution. i provided the equation

Question 2 (a) The lower yield point for an iron that has an average grain diameter of 1 x 102 mm is 230 MPa. At a grain diameter of 6 x 103 mm, the yield point increases to 275 MPa. At what grain diameter will the lower yield point be 310 MPa? (b) Predict the yield strength of the iron when the average grain diameter is 8.0 x 10-3 mm.

A hypothetical face-centred cubic metal has a lattice parameter a = 0.400 nm. A singlecrystalline bar made from the metal has a length of 20 mm and a diameter of 2 mm. TheBurgers vector of dislocations in the metal is <110>/2. Assuming only one slip system isactivated during uniform tensile straining and the angle between the direction of the Burgersvector of the dislocations and the tensile direction is 60°. Calculate the number of dislocationsneeded to achieve an engineering plastic strain of 10%. (pls give full handwritten solution to this)

A hypothetical face-centred cubic metal has a lattice parameter a = 0.400 nm. A singlecrystalline bar made from the metal has a length of 20 mm and a diameter of 2 mm. TheBurgers vector of dislocations in the metal is <110>/2. Assuming only one slip system isactivated during uniform tensile straining and the angle between the direction of the Burgersvector of the dislocations and the tensile direction is 60°. Calculate the number of dislocationsneeded to achieve an engineering plastic strain of 10%. (pls provide full calculations)

A copper-zinc alloy has the following properties: Grain Diameter (mm)              Strength (MPa)                      0.015                                       170 MPa                                 0.025                                       158 MPa                               0.035                                       151 MPa                                   0.050                                       145 MPa         Determine (a) the constants in the Hall-Petch equation; and (b) the grain size required to obtain a strength of 200 MPa.