MSE Exam 2

Explain, in terms of slip systems, why BCC and FCC metals are usually more ductile compared to HCP metals.

A metal is more ductile when it has more slip systems for dislocations to move across and FCC and BCC metals have the most slip systems with 12 each while HCP has 6 slip systems so it is the most brittle.

Define slip system and specify the characteristics of a slip system.

A slip system is the direction of movement a dislocation follows. It is made up of slip planes and slip directions which are planes and vector directions of the highest density of atoms in each of the crystal structures with the slip directions residing in each slip plane. 12 slip systems for FCC and BCC and 6 for HCP

Briefly describe the manner in which tests are performed to generate a plot of fatigue stress versus the logarithm of the number of cycles.

A specimen is subjected to a cycle of tensile, compression, bending, and twisting forces at a specific stress value and the number of cycles until fracture is recorded. Then the process is repeated with a slightly smaller stress

Describe the phenomenon of grain growth from a microscopic perspectives and cite its driving force.

After recrystallization if the material is left at an elevated temperature then the grains will continue to grow. As grain size increases the total grain boundary area decreases which decreases the total energy which is the driving force of grain growth

Describe the phenomenon of elastic recovery using a stress-strain plot.

After the load is released there is a portion of elastic recovery with the slope being parallel to the modulus of elasticity. When the load is reapplied it follows that same path but in the opposite direction

Describe edge dislocation motion by the translation of an extra half-plane of atoms as atomic bonds are repeatedly and successively broken and then reformed.

An edge dislocation moves in response to some shear force and moves parallel to the force with one plane of atoms breaking its bonds and reforming them with new atoms in the direction of the shear force. This keeps occurring like a caterpillar walking until the extra half plane of atoms is on the edge of the material.

Schematically plot both the tensile engineering stress-strain and true stress-strain behaviors for the same material and then explain the difference between the two curves.

As necking occurs there is the same amount of force applied at a smaller area so the stress increases in the true curve but that is not represented in the engineering stress strain curve. true stress = force/ instantaneous area true stress = engineering stress(1+engineering strain) True strian = ln( instantaneous length / original length)

Briefly describe the phenomenon of strain hardening in terms of dislocations and strain field interactions.

Cold work adds dislocations to the material which form repulsion strain fields with other dislocations that restrict dislocation movement. Distance between dislocations is reduced.

Given a drawing of atom positions around an edge dislocation, locate regions of compressive and tensile strains that are created in the crystal due to the presence of the dislocation.

Compression was above the perpendicular symbol where atoms were squished together. Tension was below the symbol where the atoms had space between them.

Briefly describe the two stages of crack propagation in polycrystalline materials which may ultimately lead to fatigue failure.

Crack Initiation: A small crack forms at an area of high stress concentration Crack Propagation: The crack advances incrementally with each cycle Final Failure: Occurs rapidly once the crack has reached a critical size

Describe the nature of plastic deformation, in terms of dislocation motion, for a single crystal that is pulled in tension.

Deformation will be in slip along the most favorably oriented plane and direction and occurring at different lengths along the specimen. This results in steps along the specimen that are parallel and go along the circumference of the specimen and result from the movement of a large number of dislocations along the same slip plane.

Describe the mechanism of crack propagation for both ductile and brittle modes of fracture.

Ductile crack propagation is characterized by extensive plastic deformation in the vicinity of the crack and the crack grows slowly under increasing stress. Brittle crack propagation is instant because there is little to no plastic deformation.

Give a brief definition of ductility, and schematically sketch the engineering stress-strain behaviors for both ductile and brittle materials

Ductility is a measure of how much a plastic deformation a material can undergo before fracture. %EL change in length divided by initial length * 100. %RD is change in length divided by initial length.

Explain the differences in grain structure for a metal that has been cold worked and one that has been cold worked and then recrystallized.

During cold-working, the grain structure of the metal has been distorted to accommodate the deformation. Recrystallization produces grains that are equiaxed and smaller than the parent grains

For a cylindrical specimen of a ductile material that is deformed in tension, describe how the specimen's profile changes in moving through elastic and plastic regimes of the stress-strain curve, to the point of fracture.

During the region of elastic deformation the material remains at relatively the same shape even though it is stretching slightly. Once we are between yield strength and tensile strength the material get noticeably longer and thinner. After the tensile strength point the material starts "necking" which is where the ends of the material keep their shape while the middle region of the material gets thinner and longer. This continues until fracture which is where the material breaks into two pieces.

Given values of modulus of elasticity and Poisson's ratio for an isotropic material, estimate the value of its shear modulus.

E = 2G(1+v)

Distinguish between elastic and plastic deformations, both by definition, and in terms of behavior on a stress-strain plot.

Elastic deformation is deformation under a load that when released from that load will return to its original form. In the microscopic scale this looks like the change in interatomic distances with the stretching of atomic bonds. Plastic deformation is deformation under a load that when released has caused permanent deformity to the material. In the atomic scale this looks like atoms breaking bonds with neighbors and forming bonds with new neighbors

Compute the elastic modulus from a stress-strain diagram (also tangent and secant moduli if non-linear).

Elastic modulus (E) = stress/strain. can be thought of as a materials resistance to elastic deformation. The greater the value the steeper the slope. Secant is the change stress from the origin to a point / the change in strain from the origin to a point. Tangent is the change in stress from one point to another / the change in strain from one point to another

Specify the slip systems for FCC, BCC, and HCP crystal structures.

FCC: Planes {111} with 4 different planes. Directions {110} with 3 directions in each plane. Total of 12 slip systems. BCC: Planes {110} with 6 different planes. Directions {111} with 2 directions in each plane for a total of 12 slip systems HCP: Planes {0001} with 3 planes. Directions {11-20} with 2 for each plane for a total of 6 slip systems.

HCP Slip System

Family of {0001} planes ( 3 of them) with a family of {11(-2)0} directions (2 of them) for a total of 6 slip systems

BCC Slip System

Family of {110} planes (6 of them). Family of {111} directions (2 of them) for a total of 12 slip systems.

FCC Slip System

Family of {111} planes (4 of them). Family of {110} directions (3 of them) for a total of 12 slip systems

Briefly describe what occurs during the process of recrystallization, in terms of both the alteration of microstructure and mechanical characteristics of the material and cite the driving force for recrystallization.

Formation of a new set of strain-free equiaxed grains that have low dislocation densities and are characterisitc of pre-cold worked conditions. The driving force is the difference in internal energy between the strained and unstrained material. Form as a small nuclei and grow until they consume the parent material. Mechanical characterisitcs return pre cold worked values, softer and weaker yet more ductile.

In a brief statement define fracture toughness and also specify its units. Make distinctions between stress intensity factor, fracture toughness, and plane strain fracture toughness.

Fracture toughness is the measure of a material's resistance to brittle fracture while a crack is present. Plane strain fracture toughness is the same thing but when the thickness of the material is much wider than the crack.

Define hardness in a one- or two-sentence statement and cite reasons why hardness tests are performed more frequently than any other mechanical test on metals. Schematically plot diagram tensile strength versus hardness for a typical metal.

Hardness is a measure of a material's resistance to localized plastic deformation (scratch). Test are conducted a lot because they are inexpensive, non-destructive, and other data about mechanical properties such as tensile strength can be estimated from the hardness data.

intergranular

In between the grains

Steady State Creep Rate

K1*sigma^n = steady state creep rate

Note which types of materials do, and also those which do not, experience a ductile-to-brittle transition with decreasing temperature.

Low strength metals experience a ductile to brittle transition with decreasing temperature while low strength HCP and FCC metals as well as high strength metals do not experience a ductile to brittle transformation.

Cite how elastic modulus, tensile and yield strengths, and ductility change with increasing temperature.

Modulus of elasticity, yield strength, and tensile strength decrease with an increase in temperature. Ductility increases with an increase in temperature

State what is occurring on an atomic level as a material is elastically deformed. And briefly explain how the shape of a material's force versus interatomic separation curve influences its modulus of elasticity

On the atomic scale elastic deformation is the change in interatomic distance and the stretching of atomic bonds. The magnitude of the modulus of elasticity is proportional to the slope of the force vs interatomic spacing at the equilibrium interatomic seperation

Give brief definitions of and the units for modulus of resilience and toughness (static).

Resilience is the capacity of a material to absorb energy when it is deformed elastically and then upon unloading to restore that energy. Ur = (1/2) yield strength* strain strength at yield strength. -Strain energy per unit volume Toughness is a materials ability to resistance to fracture when a crack is present. ability of a material to absorb energy and plastically deform before fracturing - energy per unit volume

Given the stress-strain behavior for two metals, determine which is the most resilient and which is the toughest.

Resilient is the most area under the origin to the yield strength while toughest is the one with the most area under the plastic curve.

Briefly state why sharp corners should be avoided in designing structures that are subjected to stresses.

Sharp corners are stress concentrates which amplify stress that make it easier for the structure to fail.

Describe the phenomenon of strain hardening (or cold-working) in terms of 1) changes in mechanical properties, and 2) stress-strain behavior.

Strain hardening is the phenomenon whereby a ductile material becomes harder and stronger as it is plastically deformed (cold working). Yield and tensile strength increase but ductility decreases. In relation to stress-strain the specimen is under stress until it starts to plastically deform then the stress is realeased and when it is reapplied there is a new and higher yield strength. Cold work imposes more dislocations which form repulsice interactions with other dislocations which restrict dislocation movement which makes the material stronger.

Briefly describe the phenomenon of solid-solution strengthening.

Strengthening metals with impurity atoms that go into either subsitutional or interstitial spots. These impurity atoms impose lattice strains on the surrounding host atoms that then interact with dislocations to restrict their movement. Small impurity atoms create tension while large impurity atoms create compression which cancel out the tension or compression stress of dislocations

Phi

The angle between the normal to the slip plane and the applied stress direction

Lambda

The angle between the slip direction and the applied stress direction

Briefly describe how plastic deformation occurs by the movement of both edge and screw dislocations in response to applied shear stresses.

The edge dislocations move like a caterpillar in the direction of shear stress and cause the extra half plane of atoms to move to the edge of the material in a line. Screw dislocations break bonds on one end of the plane and move and form bonds in the direction of the shear force one by one.

Briefly explain how the grain structure of a poly crystalline metal is altered when it is plastically deformed.

The grains go from being equiaxed ( or generally similar in width and length) to being stretched in the direction of the stress applied the specimen.

Explain why engineering stress decreases with increasing engineering strain past the tensile strength point.

The material begins necking so overall the strain on the entire material is less

Tensile Stength

The resistance of a material to breaking under tensile forces. Maximum value of stress on a engineering stress-strain curve

Critical Resolved Shear Stress

The shear stress, resolved within a slip plane and direction, required to initiate slip. Determines when yielding occurs

Given the stress-strain behavior for two metals, be able to distinguish which is stronger

The stronger metal is the one with the higher yield strength

Yield Strength

The value of stress when a certain amount of plastic deformation occurs. Offset of .002 strain and then drawn with the same slope as elastic modulus until it hits the curve. yield strength = critical resolved shear stress/ ( Cos(phi)*Cos(lambda))max

Explain why the strengths of brittle materials are much lower than predicted by theoretical calculations.

There are flaws inside brittle materials that amplify stress which cause the material to fracture earlier than the theoretical value that did not account for a flaw

Creep

Time dependent permanent deformation of materials under a constant stress at high temperatures.

Given values of the constants K and n in the equation relating plastic true stress and true strain, be able to compute the true stress necessary to produce some specified true strain

True stress = K*true strain^n

Describe how grain boundaries impede dislocation motion and why a metal having small grains is stronger than one having large grains.

Two adjacent grains have different orientations and the grain boundary between them is where they change orientations. This change in orientation requires a change in direction of dislocation motion that becomes harder to pull off as crystallographic misorientation increases. Also the atomic disorder in a grain boundary results in a discontinuity of slip planes. small grain materials are stronger because they have a higher total grain boundary area.

List and briefly describe the two atomic mechanisms of diffusion and indicate which type of diffusion occurs more rapidly, and then explain why this is so.

Vacancy diffusion occurs when atoms move from one lattice site to another lattice site that is empty. Interstitial diffusion occurs when atoms diffuse into the interstitial sites between lattice sites. Interstitial diffusion occurs more rapidly because there are more interstitial sites and the smaller atoms can move more freely.

Explain why and describe how the yield strength of a metal is related to the ability of dislocations to move.

Yield strength is a measure of when a certian amount of plastic deformation occurs and plastic deformation corresponds to the movement of a large number of dislocations so if dislocation movement is hindered or restricted then the yield strength of a material becomes greater. And vice versa, the easier it is for dislocation movement to occur the weaker a material is and the smaller the yield strength is.

Cite which tensile parameters are sensitive (and also which are insensitive) to any prior deformation, the presence of impurities, and/or any heat treatment.

Yield strength, tensile strength, and ductility are sensitive to prior deformation, heat treatment, and impurities. Modulus of elasticity is not sensitive to these.

Toughness

ability of a material to absorb energy and plastically deform before fracturing. Area underneath the plastic part of curve

Resilience

ability of a material to absorb energy under elastic deformation and then to release that energy when unloaded. Area under the elastic part of the engineering stress strain curve.

Make a schematic plot of how the room temperature tensile strength and ductility vary with temperature (at a constant heat-treating time) in the vicinity of the recrystallization temperature, for a metal that was previously cold-worked. Define recrystallization temperature.

as temperature increases the ductility increases but the strength of the material decreases. the temperature at which recrystalization takes 1 hour

Cite the conditions that must be met in order for a brittle material to experience fracture.

crack stress = (2EY/(pi)a)^(1/2)

Determine the engineering stress and engineering strain for a tensile test specimen with given initial/instantaneous length and cross-sectional dimensions.

engineering stress (sigma) = Force/ area - MPa engineering strain (curvy e) = change in length/ original length - unit less

Fatigue

form of failure that occurs in structures subjected to dynamic and fluctuating stresses after a lengthy period of stress-strain cycling.

Intragranular or Transgranular

passes through the grains

Resolved Shear Stress (τR)

shear stress components applied in directions all but parallel and perpendicular to the tensile or compression stress being applied. Their magnitude relies on the magnitude of the tensile or compression stress and the orientation of the slip plane and slip direction. Sigma(Cos(phi)*Cos(Lambda))

Briefly describe the changes that take place as a metal experiences recovery.

some of the stored internal strain energy is relieved by virtue of dislocation motion that results from increased atomic diffusion that results from an increase in temperature. There is a reduction in the # of dislocations and they have low strain energies

Given Poisson's ratio and the elastic strain in the direction of the applied load (i.e., axial strain), be able to compute the elastic strain in the lateral (or perpendicular) direction.

v = -(strain x / strain z) or -(strain y / strain z)