Week 1. Flashcards
What is the definition of force?
The product of mass and acceleration.
What is a direct force?
A force that is normal to the surface it is applied.
What are the two types of direct force?
Tensile or compressive.
What is shear force?
A force that tends to tear the member into two and makes the layers of the particles of a body slide over each other.
What is the definition of engineering stress?
Engineering Stress = Force (F) / Original Cross-sectional Area (A)
What are the two types of stress?
Direct or Shear
What are the two types of direct stress?
Compressive or tensile
How is engineering strain defined?
Engineering strain is the increase in length per unit original length.
What is the formula for calculating engineering strain?
Strain = (change in length) / (original length).
What are the two types of engineering strain?
Tensile and Compressive.
What does Hooke’s Law state?
Stress is proportional to strain.
How is stress related to strain in Hooke’s Law?
Stress = E * Strain, where E is the Young’s Modulus of Elasticity.
What is the constant of proportionality in Hooke’s Law called?
Young’s Modulus of Elasticity (E).
What are the three types of static stresses to which materials can be subjected?
- Tensile - tend to stretch the material
- Compressive - tend to squeeze it
- Shear - tend to cause adjacent portions of material to slide against each other
What is a stress-strain curve?
It is the basic relationship that describes mechanical properties for all three types of stresses.
What is the tensile test commonly used for studying?
Stress-strain relationship, especially in metals.
What happens to the material during a tensile test?
It is elongated and its diameter is reduced.
What does ASTM stand for?
American Society for Testing and Materials.
What does ASTM specify the preparation of?
Test specimen.
What is the purpose of a tensile test?
To determine the mechanical properties of materials.
What is shown in Figure 3.1 of the document?
A typical test specimen for a tensile test.
What is the typical progress of a tensile test?
1) Beginning of test, no load
What happens if pieces are put back together after fracture in a tensile test?
The final length can be measured.
What does a compression test apply to a cylindrical specimen?
A load that squeezes the ends between two platens.
How is the compression force applied to the test piece?
Between two platens.
What is the resulting change in height during a compression test?
It decreases.
How is engineering stress in tension defined?
As force divided by original area.
What does the symbol ‘F’ represent in the equation for engineering stress?
Applied force.
What does the symbol ‘Ao’ represent in the equation for engineering stress?
Original area of the test specimen.
What happens to the height of the specimen during compression?
It is reduced.
How does the cross-sectional area change during compression?
It is increased.
What does the symbol A_o represent in the equation for engineering stress in compression?
Original area of the specimen.
How is engineering strain defined in tension?
e = (L - L0) / L0
How is engineering strain defined in compression?
As the reduction in height, resulting in a negative value of strain.
What is the value of engineering strain in compression?
Negative (the negative sign is usually ignored when expressing compression strain).
How is the shape of the plastic region different in a compression test compared to a tensile test?
The cross-section increases in a compression test.
Is the calculated value of engineering stress higher in a compression test or a tensile test?
Higher in a compression test.
What type of test is represented by the engineering stress-strain curve in Figure 3.8?
Compression test.
What does the elastic region of the stress-strain curve indicate?
It is the region prior to yielding of the material.
What does the plastic region of the stress-strain curve indicate?
It is the region after yielding of the material.
What is the Elastic Region in Stress-Strain Curve?
The relationship between stress and strain is linear.
What happens to the material when stress is removed in the Elastic Region?
The material returns to its original length.
What is Hooke’s Law?
σe = Ee, where E is the modulus of elasticity.
What does the modulus of elasticity (E) measure?
The inherent stiffness of a material.
How does the value of modulus of elasticity (E) differ for different materials?
Its value differs for different materials.
What is the Yield Point in a stress-strain curve?
The point at which the material begins to yield and the linear relationship changes slope at the upper end of the linear region.
How is the Yield Point identified?
By the change in slope at the upper end of the linear region.
What is another name for the Yield Point?
Yield strength, yield stress, and elastic limit.
What happens at the Yield Point in terms of strain?
0.2% permanent set of strain or 0.002 strain offset, meaning the material won’t return to its original length.
How is the Young’s Modulus value calculated at the Yield Point?
By subtracting 0.002 from the strain value of the yield point to get the strain which corresponds to the Young’s Modulus value.
What is the modulus of elasticity of the material?
Change in stress / Change in strain
How is tensile strength determined?
By dividing the maximum load by the original cross-sectional area of the specimen.
What is the percent elongation if fracture occurs at a gage length of 7.4 cm?
((7.4 - 5) / 5) * 100%
How is the percent reduction in area determined if the specimen necked to an area of 1.56 cm^2?
((3.125 - 1.56) / 3.125) * 100%
What does AR stand for and how to calculate it?
AR = (Ao - Af) / Af
What does the yield point mark in the stress-strain curve?
The beginning of plastic deformation.
What law is no longer guided beyond the yield point in the stress-strain relationship?
Hooke’s Law.
What happens to the elongation rate beyond the yield point?
It proceeds at a much faster rate than before.
How does the slope of the stress-strain curve change beyond the yield point?
It changes dramatically.
What happens to the cross-sectional area during elongation in a tensile test?
It undergoes a uniform reduction.
What is the engineering stress at the point where the applied load reaches a maximum?
Tensile strength or ultimate tensile strength.
How is the ultimate tensile strength (TS) defined?
TS = F max / A
What is ductility in the context of a tensile test?
The ability of a material to plastically strain without fracture.
How is elongation (EL) calculated in a tensile test?
EL = (L - Lo) / Lo, where L is the specimen length at fracture and Lo is the original specimen length.
How is true stress calculated?
True stress is obtained by dividing the instantaneous area into the applied load.
What does true strain provide a more realistic assessment of?
Instantaneous elongation per unit length.
What type of stress-strain values were used to plot the previous curves?
True stress and strain values.
What department at Stellenbosch University is associated with this information?
Industrial Engineering Department.
What happens to true stress in the plastic region until necking?
It increases continuously.
Why was the significance of strain hardening lost in the engineering stress - strain curve?
Because stress was based on an incorrect area value.
What does it mean when a metal is becoming stronger as strain increases?
It exhibits strain hardening.
What happens to the plastic region of the true stress-strain curve when plotted on a log-log scale?
It becomes linear.
What is the relationship between true stress and true strain in the plastic region?
It is a straight line in a log-log plot.
What does the symbol ‘K’ represent in the flow curve equation?
Strength coefficient.
What does the symbol ‘n’ represent in the flow curve equation?
Strain hardening exponent.
What is the formula for the flow curve equation in a tensile test?
σ = Kε^n
What does ‘K’ represent in the flow curve equation?
The strength coefficient.
What does ‘n’ represent in the flow curve equation?
The strain-hardening exponent.
How is the strength coefficient (K) calculated in the flow curve equation?
K = σ/ε^n
How is the strain-hardening exponent (n) calculated in the flow curve equation?
n = ln(σ2/σ1) / ln(ε2/ε1)
What are the differences between engineering stress-strain curves in tension and compression?
Although differences exist, the true stress-strain relationships are nearly identical.
How are flow curve values from tensile test data applied to compression operations?
The flow curve values (K and n) from tensile test data can be applied to compression operations.
What phenomenon should be ignored when using tensile K and n data for compression?
Necking, which is peculiar to straining induced by tensile stresses.
What are the categories of Stress-Strain Relationship?
- Perfectly elastic, 2. Elastic and perfectly plastic, 3. Elastic and strain hardening.
What defines the behavior completely?
Modulus of elasticity (E).
What happens to materials defined by modulus of elasticity (E) when stressed?
They fracture rather than yielding to plastic flow.
What type of materials are considered brittle?
Ceramics, many cast irons, and thermosetting polymers.
What are the three categories of stress - strain relationship?
Perfectly elastic, perfectly plastic, and strain hardening.
What is the symbol used to represent stiffness?
E.
What happens to a material once it reaches the yield point?
It deforms plastically at the same stress level.
What are the values of K and n in the flow curve when a material behaves elastically and perfectly plastically?
K = Y, n = 0.
When do metals behave like elastic and perfectly plastic materials?
When heated to sufficiently high temperatures (above recrystallization).
What does Hooke’s Law describe in the elastic region?
The relationship between stress and strain.
What does a flow curve with K > Y and n > 0 indicate?
Most ductile metals behaving this way when cold worked.
In which category of stress-strain relationship does elastic and strain hardening fall?
Elastic and Strain Hardening.
What type of materials are often tested by a bending test?
Hard brittle materials (e.g., ceramics).
What is another name for the bending test?
Flexure test.
How is the specimen positioned in a bending test?
Between two supports, with a load applied at its center.
What happens to brittle materials before fracture?
They deform elastically until fracture.
How does failure occur in brittle materials?
Failure occurs because tensile strength of outer fibers of specimen are exceeded.
What is the common failure type with ceramics and metals at low temperatures?
Cleavage, in which separation rather than slip occurs along certain crystallographic planes.
What is Transverse Rupture Strength (TRS) derived from?
The bending test.
How is Transverse Rupture Strength (TRS) calculated?
TRS = F / (b * t)
What does ‘F’ represent in the TRS formula?
Applied load at fracture.
What does ‘L’ represent in the TRS formula?
Length of specimen between supports.
How is shear stress defined?
Shear stress is defined as F/A, where F = applied force and A = area over which deflection occurs.
How is shear strain defined?
Shear strain is defined as δ/b, where δ = deflection element and b = distance over which deflection occurs.
What is the relationship for shear elastic stress-strain in the elastic region?
G = shear modulus, where G = 0.4E for most materials.
What is the relationship between shear plastic stress and strain?
Similar to the flow curve.
How can shear strength be estimated from tensile strength?
Shear strength ≈ 0.7 * Tensile Strength.
What type of stress-strain curve is the engineering stress-strain curve for shear similar to?
True stress-strain curve.
What is the formula for calculating the factor of safety?
Factor of safety = Yield stress / Working stress.
How is working stress defined?
The stress a component is subjected to during its day-to-day usage.
What is the purpose of incorporating a factor of safety in a component’s design?
To avoid premature failure of the component.
What is hardness in materials?
Resistance to permanent indentation.
What does good hardness in a material indicate?
Resistance to scratching and wear.
Why must most tooling used in manufacturing be hard?
For scratch and wear resistance.
Why are hardness tests commonly used for assessing material properties?
Because they are quick and convenient.
Why are a variety of testing methods appropriate for hardness tests?
Due to differences in hardness among different materials.
What are the most well-known hardness tests?
Brinell and Rockwell.
Apart from Brinell and Rockwell, what are some other hardness test methods?
Vickers, Knoop, Scleroscope, and durometer.
What is the load used in Brinell hardness testing?
500, 1500, or 3000 kg.
What type of specimen surface is a hard ball pressed into in Brinell hardness testing?
Specimen surface of metals and nonmetals of low to medium hardness.
What is the name of the hardness testing method where a hard ball is pressed into the specimen surface?
Brinell hardness testing.
What is the formula for calculating Brinell Hardness Number (BHN)?
HB = F / (π * D * (D - sqrt(D^2 - d^2))),
where HB is the Brinell Hardness Number,
F is the indentation load in kg,
D is the diameter of the ball in mm,
d is the diameter of the indentation in mm.
What is the Rockwell Hardness Test?
A widely used test where a cone-shaped indenter is pressed into a specimen using a minor load of 10 kg followed by a major load of 150 kg.
What is the purpose of the minor load in the Rockwell Hardness Test?
To seat the indenter in the material.
What happens when the major load is applied in the Rockwell Hardness Test?
It causes the indenter to penetrate beyond its initial position.
How is the Rockwell hardness reading determined?
By converting the additional penetration distance (d) into a reading using the testing machine.
What is hot hardness?
The ability of a material to retain hardness at elevated temperatures.
What does hot hardness measure?
The ability of a material to maintain its hardness at elevated temperatures.
Why is hot hardness important in manufacturing processes?
It ensures that materials maintain their hardness at high temperatures.
What is recrystallization in metals?
The formation of new grains that are free of strain when a metal is heated to a sufficiently high temperature and deformed.
What happens to the strain hardening of metals when heated to a sufficiently high temperature?
Strain hardening does not occur, and the metal behaves as a perfectly plastic material with n = 0.
How do most metals behave at room temperature according to the flow curve?
Most metals strain harden at room temperature (n > 0).
What is recrystallization in metals?
Formation of new strain-free grains.
How is the recrystallization temperature of a metal related to its melting point?
About one-half of its melting point (0.5 Tm) on an absolute temperature scale.
How is the recrystallization temperature specified?
As the temperature at which new grains are formed in about one hour.
What is recrystallization in the context of manufacturing?
Heating a metal to its recrystallization temperature prior to deformation.
What are the advantages of heating a metal to its recrystallization temperature before deformation?
Allows a greater amount of straining and requires lower forces and power for the process.
What is the term for forming metals at temperatures above the recrystallization temperature?
Hot working.
What do mechanical properties determine in a material?
A material’s behavior when subjected to mechanical stresses.
What are some examples of mechanical properties?
Elastic modulus, ductility, hardness, and various measures of strength.
What is the dilemma related to mechanical properties in design and manufacturing?
Desirable mechanical properties for high strength usually make manufacturing more difficult.
What should the manufacturing engineer appreciate in relation to the design viewpoint?
The desirable mechanical properties for high strength.
What should the designer be aware of in relation to the manufacturing viewpoint?
The impact of desirable mechanical properties on manufacturing difficulty.
