Mechanical Behavior PDF

Materials and Manufacturing Processes (Nuclear Engineering) 4EN514 derby.ac.u k Relevant KSB for this topic: SK2, SK3, SK7, SK8, B3, B5 derby.ac.u k...

Materials and Manufacturing Processes (Nuclear Engineering) 4EN514 derby.ac.u k Relevant KSB for this topic: SK2, SK3, SK7, SK8, B3, B5 derby.ac.u k 2 Mechanical Behavior derby.ac.u k 3  Objectives  What is the strength of a structural material?  How much deformation can a structural material withstand for a given load?  Investigate how materials deform (elongate, compress, twist) or break as a function of applied load, time, temperature, and other conditions  Discuss standard test methods and standard language for mechanical properties of materials derby.ac.u k 4  Examples Materials for aircrafts such as Aluminum and carbon- fiber-reinforced composites must be strong, light and withstand cyclic loading. Materials for sports must be light and be able to take many impact loadings. derby.ac.u k 5  Mechanical Properties of Solids - Terminology We select a material for a component by matching its mechanical properties to the service condition required of the part. We have to determine if it should be stiff, strong, or ductile. Will it be subjected to repeated applications of a high force? Will it have to operate at elevated temperatures or low temperatures? We usually require the results of tests that have determined how a material withstands an applied force. – The results for such tests are the mechanicalderby.ac.u k 6 properties of the material.  Things Related to Mechanical Behavior Material nature Ductile versus brittle fracture Static versus cyclic loading Deformation mechanisms Deformation mechanisms Creep deformation (stress and temperature effects) Fatigue fracture (high cycle vs. low cycle) derby.ac.u Notch sensitivity and loading directions k 7  Mechanical Testing of Materials Test type/loading Test specimen o Tension o Un-notched o Compression o Notched (Any stress o Hardness raiser, hole, groove, o Bending cracks …) o Torsion Test standards Environmental o Industry conditions o Company o Test ambient Test Equipment o Specimen derby.ac.u k 8 Types of Mechanical Loadings derby.ac.u k 9  Standard Test Methods Mechanical testing o Material properties as input for design procedure o Quality control Test standards provide consistency, user- producer communication Professional societies: o American Society for Testing and Materials - ASTM o International Organization for Standardization – ISO o European Norms- EN / BS o DIN derby.ac.u k 10 Standard Test Methods Annual Book of ASTM (American Society for Testing Materials) standards covers significant number of standards for mechanical testing-about 10 volumes Test standards organized by class of material Metals, concrete, plastics, rubber, glass... derby.ac.u k 11 Standards for Test Methods derby.ac.u Source of Table: Mechanical Behaviour of Materials, N. E. k 12 Dowling  Standards or Specifications for Test Methods Provide procedures to be followed in detail o Specimen description o Loading conditions o Values to report o Statistical analysis derby.ac.u k 13 Mechanical Testing derby.ac.u k 14  Uniaxial Tension Test The tensile test measures the resistance of a material to deform when a static or a force is slowly applied. A universal tensile testing machine is used to measure the stress-strain response of a material. A unidirectional force, or load, is applied and a strain gage or extensometer is used to measure derby.ac.u the strain. k 15  Concept of Stress Typical engineering viewpoint: Forces are input, Structure/component is the system; Effects of forces on the system are output, e.g. Deformations, cracking, failure  F A (in Pa or MPa) Test set 1: Bars of same elastic material and cross sectional area A, but different sectional shapes Tension test: pulled from both ends Result: they fail approximately at the same final load or tensile force, F. The length has no appreciable effect on the failure force. The shape and length of the bar is immaterial. derby.ac.u k 16  Concept of Stress Test set 2: Bars of same elastic material and cross sectional area 2A (twice as much as for the bars in test set 1), but different sectional shapes Tension test: pulled from both ends Result: they fail approximately the same final load or tensile force, Doubling 2F the cross-sectional area doubles the failure load or force. The ratio of Force to Area remains the same!!! Stress: Primary means of predicting the behavior of structure and materials Stress describes the intensity of the force or the amount of the force carried by each unit of areas, and a derby.ac.u measureable parameter of material to carry the forces:k 17 Uniaxial Tension Test Sample Pulling a sample of material in tension until fracture Specimens designed to avoid break where gripped F ric tio n D ia d g rip s P P g a u g e le n g th P in e n d S trip UTAS derby.ac.u k 18   l f  lo  l Engineering Strain :      lo  lo where l f is final lenght, and lois initial lenght Engineering Stress :  F / Ao F applied load perpendicular to specimen cross-section; Ao is cross-sectional area perpendicular to the force before the application of the load These definitions of stress and strain allow one to compare test results for specimens of different cross-sectional area A0 and of different length l0. derby.ac.u k 19  Uniaxial Tension Test Strain or load controlled o Usually constant Crosshead speed, mm/min Report stress-strain curve until failure Ideally recorded by dedicated transducers o Extensometer Tensile Testing a Stainless Steel o Strain gages bonded on the specimen Tensile Specimen - YouTube o Digital image correlation (DIC) derby.ac.u k 20 Mechanical Properties of Solids - Terminology  E  derby.ac.u k 21 Mechanical Properties of Solids - Terminology Elastic deformation or elastic strain is defined as fully recoverable strain resulting from an applied stress. Young’s modulus or modulus of elasticity is the slope of a tensile stress-strain curve in the linear region. The inverse of Young’s modulus is known as the compliance of the material. Plastic Deformation or plastic strain is permanent deformation remaining after removal of a stress, i.e., the material doesn’t go back to its original shape. Yield strength is the stress at which plastic deformation becomes noticeable. It is the stress that generates 0.2 % derby.ac.u permanent deformation. k 22  Yield Strength Sometimes for certain materials, it is difficult to specify precisely the point at which the stress-strain curve deviates from linearity and enters the plastic region. Yield strength: It is the stress that generates 0.2 % permanent deformation. derby.ac.u k 23  Offset Yield Strength Stress Proof Strength  Locate C at 0.2%(or D 0.1%) strain  Draw CD // to AB B  The Proof Strength is stress at D  Proof Strength is Strain sometimes called the C 0.2% (or 0.1%) offset A Yield strength 0.002 strain  Only req’d when well defined yield cannot be determined derby.ac.u k 24  Young’s modulus Young’s modulus is the modulus of elasticity. It is the slope of the stress-strain curve in the elastic region. It is usually referred to as “E” but sometimes as “Y” in the published literature. It shows the resistance of the metal to permanent deformation and also indicates the ease with which the metal can be deformed by rolling or drawing operations. It is closely related to the binding energies of the atoms in materials. It is also closely related to the “stiffness” of a material – higher E means a stiffer derby.ac.u k 25  More terminology At the ultimate T.S, the sample begins to neck Toughness d down Tensile strength or Ultimate Strength is the stress obtained at the highest applied force. In some ductile materials, “necking” or a narrowing of the sample occurs. The tensile strength can be defined as the stress at which necking begins in ductile materials. derby.ac.u k 26  More terminology Residual stress: it is the stress remaining within a structural material after all applied loads have been removed. Strain hardening: Within the region of the stress-strain curve between Y.S and T.S, the phenomenon of increasing strength with increasing deformation is referred to as strain hardening. Cold working: the plastic deformation well-below derby.ac.u one k 27  True stress versus Engineering stress It might appear that plastic deformation beyond T.S softens the material because the engineering stress falls down. Instead this drop in stress is due to the fact that engineering stress and strain are defined relative to dl dl d T  d T original  sample l l dimensions. l f dl l l  l  l l   T   ln f ln i ln  i   ln(1   ) il l li li  li li  No practical difference between engineering stress & true stress and engineering strain & true strain in the linear region. Note that engineering stress-strain are most appropriate for small strains where the changes in area and length are specifically considered. derby.ac.u k 28  True stress versus Engineering stress: Strain hardening 𝜎 =𝐹 / 𝐴 𝑇 exponent The curve 𝑎𝑐𝑡𝑢𝑎𝑙 between the onset of the plastic deformation (Y.S.) and the onset of necking (T.S.) can be approximated by 𝑛 𝜎 𝑇 =𝐾 𝜀 𝑇 where n and K are constants The slope of the log-log plot is the parameter n which is referred to as strain hardening exponent. For low carbon steels, n= 0.22. Higher values up to 0.26 indicates an improved ability to be deformed during the shaping process without excess thinning or fracture of the piece. For perfect plastic materials n=0 , For perfect elastic material n=1. derby.ac.u k 29  Strain Hardening A ductile material becomes harder and stronger as it is plastically deformed. This is referred to as strain hardening or work hardening. Strain hardening mechanism: This involves dislocation – dislocation interactions Every dislocation produces a strain field around its line. On average, dislocation – dislocation strain interactions are repulsive, i.e., the motion of a dislocation will be hindered by the presence of other dislocations. Plastic deformation increases the density of dislocations, which increases the resistance to dislocation motion. The strength of the material increases at the expense of ductility, which decreases. derby.ac.u k 30  Strain Hardening Strain hardening shown by use of the stress-strain curves. A specimen is stressed beyond the yield curve so plastic deformation results. Next time the specimen is stressed, it follows a new curve and begins to deform at a higher stress level. By repeating the procedure, the strength continues to increase but the ductility decreases. derby.ac.u k 31  Necking Localized deformation of a ductile material produces necking. The true stress-strain takes into account the reduction of area and the increase in stress on the material due to necking. derby.ac.u k 32  True stress vs Engineering stress Engineering stress & strain are based on original areas and lengths Engineering stress and strain appropriate when the changes in specimen dimensions are small such as area True stress & strain are based on actual areas and lengths For ductile materials, in particular, true stress- derby.ac.u strain differs from engineering stress-strain k 33 Ductility & Toughness Ductility: the percent elongation at failure. The value of percent elongation at failure is a function of gage length. The tabulated values are generally given for the gage length of 2 inch. High ductility Ductility implies 100  failure ease at deformation. Toughness: If the alloy is both ductile and strong, it is said to be tough. (Ability of the material to absorb energy without fracture) derby.ac.u k 34  Ductility and Temperature High ductility is desired because it ensures: Good resistance to crack propagation Good fabricability Ductility is a critical property for cryogenic applications. In general, BCC metals such as Fe, Carbon and low-alloy steels, Molybdenum, and Niobium become brittle at low temperatures. FCC metals such as Cu, Ni, Cu-Ni alloys, Al and its alloys, and austenitic stainless steels remain ductile at low temperatures. Most plastics and elastomers become brittle at low temperatures. Ceramics and glasses are already brittle at room temperature and become slightly more so at cryogenic derby.ac.u k 35 temperatures. Upper and lower yield points for a low carbon steelpoint is associated with non- The ripple pattern at the yield homogeneous deformation that begins at a point of stress concentration often near the specimen grip. The upper yield point in steel exists because interstitial carbon pins the core of the dislocations. Once the dislocations break free of the carbon then yield can occur at a lower stress, i.e., lower yield point. derby.ac.u Uniaxial Tensile Test: http://www.msm.cam.ac.uk/doitpoms/tlplib/mechanical-testing/index.php k 36 Other elastic constants  F / As ,  tan  y / zo , G  /  For isotropic material : E 2G 1  υ   G shear modulus N / m 2   shear stress As area parallel to the applied load  shear strain  angular displaceme nt derby.ac.u k 37 Poisson’s ratio and shear modulus derby.ac.u k 38  Brittle vs Ductile behavior Stress-strain behavior varies widely Brittle behavior: without extensive deformation-gray cast iron, some polymers (PMMA), glass Ductile behavior: failure following extensive deformation-metals derby.ac.u k 39 Ceramics and Glasses derby.ac.u k 40 Brittle fracture: Ceramic and glasses In general, ceramics shows no plastic deformation, shows brittle fracture, and performs better under the compression loads derby.ac.u k 41  Brittle Materials In brittle materials the fracture occurs at the maximum load, which is the same as the yield strength, tensile strength and breaking strength. Yield in brittle materials such as ceramics does not occur by the motion of dislocations but by planar defects such as cracks. The stress-strain behavior of brittle materials compared to that of more ductile materials. derby.ac.u k 42  Brittle Materials The bend test is used to measure the properties of brittle materials where a flat specimen is put under load and bent. The bend test for measuring the strength of brittle materials and the deflection, d, obtained by bending. The modulus of elasticity in bending or the flexural modulus is given by, L3 F L3 m Ebend   4 wh  4 wh3 3 The maximum flexural stress (modulus of rupture) for a three point bend test is given by, 3FL  bend  2 wh 2 Flexural strength is similar in magnitude to the tensile strength as the failure mode in bending is tensile along the outermost edge of the sample derby.ac.u k 43 Brittle Materials The stress-deflection curve for MgO obtained from a bend test. derby.ac.u k 44  Modulus of Elasticity and strength (Modulus of Rupture) for some ceramics and glasses derby.ac.u k 45 Poisson’s ratio for some ceramics and glasses 1 1 For metals, υ  , for ceramics, υ  3 4 derby.ac.u k 46  Stresses at crack tips in Brittle materials: such as Underlying reason structural ceramics Ceramics for mechanical behavior of Flaws are inevitable in routine production and handling of ceramics and glasses Griffith assumed numerous elliptical cracks at the surface and/or interior The highest stress occurs at the 1/ 2 crack tip (in tension) c  m 2    Note: crack-tip radius ρ can be as small as inter-atomic spacing  very high σm Hence, these materials are relatively weak in tension. A compressive load tends to close the Griffith flaws, thereby not diminishing the inherent strength of derby.ac.u ionically and covalently bonded materials. k 47 Stresses at crack tips in Brittle materials: such as Ceramics derby.ac.u k 48  Why ceramics are brittle Difficulty in creating obstacle free slip planes many slip planes are not possible due to the charged state of ions. The sliding of ions with like charges past one another can result in high repulsive forces. Manufacturing defects with sharp crack tips (stress concentration) derby.ac.u k 49 Group Assignment derby.ac.u k 50  Hardness Test A qualitative indication of strength of materials (a simple alternative to the tensile test) Hardness is the property of a material that enables it to resist plastic deformation, usually by penetration. However, the term hardness may also refer to resistance to scratching, abrasion or cutting. Several types, usually for metals Indentation hardness: pressing of a hard indenter against the sample with a known force Scleroscope hardness test: a hardness test in which a diamond pointed hammer is dropped onto metal and the height of the bounce is measured. A modified version is also for polymers Mohs hardness: used in mineralogy. Scratching, matter of judgment, scaled derby.ac.u between 1-10, (soft mineral talc – diamond, k 51  Relationship between Strength & Hardness The hardness test is really a strength test P P Hardness Test Uniaxial Compression Test Restraint No Restraint There are correlations between tensile strength (rather than yield strength) and hardness for many materials because hardness tests involve a large amount of plastic deformation derby.ac.u k 52 Common types of Hardness Test and Geometries derby.ac.u k 53 derby.ac.u k 54  Creep: plastic deformation occurring at high temperature derby.ac.u k 55  Creep Below yield strength at RT, the strain generally does not change with time under a fixed load. Repeating this experiment at a high temperature (T > Tmelt /3 or Tmelt /2) produces different results. Creep  plastic deformation occurring at high temperature (T > Tmelt /3 or Tmelt /2 under constant load over a long period in time, e.g. turbine blades, steam generators  Creep shortens the life of a component Creep testing derby.ac.u k 56  Creep stages The primary Rapid increase in the length stage: due to enhanced deformation Decreasing mechanisms such as strain rate dislocation climb. The (slope) deformation is enhanced due to thermally activated atom mobility, which provides dislocations with additional slip planes to move The secondary The increase ease of slip due stage: Steady to high temperature mobility is state creep: balanced by increasing constant resistance to slip due to strain rate dislocation pile-up, or other microstructural obstacles The tertiary Strain rate increases due to an stage: increase in true stress related Increasing to cross-sectional area strain rate reduction, internal cracking, derby.ac.u grain boundary separation, k 57  Dislocation Climb in Creep During creep, atoms and vacancies diffuse and react with dislocations, which enables the dislocations to climb in response to the applied stress. derby.ac.u k 58  Variation of the creep curve with stress and temperature Look at the slopes Creep is a thermally activated process  Arrhenius behavior −𝑸 / 𝑹𝑻 𝜺=𝑪 ˙ 𝒆 derby.ac.u k 59 Creep Important usage of Arrhenius equation: High temperature strain data collected in short- time can be used to predict long-term creep behavior at lower service temperature. The extrapolation is valid as long as the same creep mechanism operates over the entire temperature range −𝑄/ 𝑅𝑇 𝜀=𝐶 ˙ 𝑒 derby.ac.u k 60 Group Assignment derby.ac.u k 61  Creep of Ceramics Ceramics are used at high temperature much more widely. Creep becomes important for ceramics. Diffusion mechanism in the creep of ceramics is more complex than in the case of metals because of the requirement of charge neutrality and different diffusivities for cations and anions. As a result, grain boundaries are important for the creep of ceramics because adjacent grains slide along these boundaries (creep due to grain boundary sliding is undesirable due to the resulting weakness at highderby.ac.u k 62 temperature).  Creep Deformation mechanisms involved in creep include: Dislocations : slip Vacancies or atoms : diffusion Grain boundaries : grain rotation, grain boundary sliding Only solid solution hardening and precipitation hardening remain effective at elevated temperatures to help prevent creep. Grain boundary sliding during creep causes a) the creation of voids at an inclusion trapped at the grain boundary b) the creation of a void at a triple point where 3 grains are derby.ac.u in contact. k 63  Fatigue Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stresses (e.g., bridges, aircraft, and machine components). Under these circumstances it is possible for failure to occur at a stress level considerably lower than the tensile or yield strength for a static load. The term fatigue is used because this type of failure normally occurs after a lengthy period of repeated stress or strain cycling. The surface which has undergone fatigue fracture appears brittle without gross deformation at fracture (in the macroscale). On a macroscopic scale the fracture surface is usually derby.ac.u normal to the direction of the principal tensile stress. k 64  Cyclic stresses The applied stress may be axial (tension– compression), flexural (bending), or torsional (twisting) in nature. Three different fluctuating stress–time modes are possible. 1. Completely reversed cycle of stress(repeated stress cycle): the amplitude is symmetrical about a mean zero stress level, for example, alternating from a maximum tensile stress to a minimum compressive stress of equal magnitude. 2. purely tensile cycle or purely compressive cycle: the maxima and minima are asymmetrical relative to the zero-stress level. 3. Random cycle: the stress level may vary derby.ac.u k 65 randomly in amplitude and frequency.  Important fatigue Mean stress 𝜎 , defined as the average of the maximum parameters 𝑚 and minimum stresses in the cycle 𝜎 𝑚𝑎𝑥 + 𝜎 𝑚𝑖𝑛 𝜎 𝑚= 2 Range of stress 𝜎𝑟 , defined as the difference between maximum and minimum value of stresses in the cycle 𝜎 =𝜎𝑟 Stress amplitude is just one-half of this range of stress 𝜎 𝜎 −𝜎 𝑟 𝑚𝑎𝑥 𝑚𝑖𝑛 𝜎 𝑎= = 2 2 Stress ratio R is just the ratio of minimum and maximum stress amplitudes. 𝜎 𝑚𝑖𝑛 𝜎𝑎 1 − 𝑅 𝑆𝑡𝑟𝑒𝑠𝑠 𝑟𝑎𝑡𝑖𝑜𝑛 → 𝑅= 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑟𝑎𝑡𝑖𝑜 → 𝐴= = 𝜎 𝑚𝑎𝑥 𝜎𝑚 1+ 𝑅 derby.ac.u k 66  Important fatigue parameters (a) Reversed stress cycle, in which the stress alternates from a (b) Repeated stress cycle, in which maximum and minimum maximum tensile stress to a maximum compressive stress of stresses are asymmetrical relative to the zero-stress level equal magnitude. (c) Random stress cycle. derby.ac.u k 67  S-N curve Engineering fatigue data is usually plotted as a S-N curve. Here S is the stress and N the number of cycles to failure (usually fracture). The x-axis is plotted as log(N). The stress plotted could be one of the following: , ,. Each plot is for a constant, Most R orexperiments fatigue A. are performed with m = 0 (e.g. rotating beam tests). Typically the stress value chosen for the stress is low (< y) and hence S- N curves deal with fatigue failure at a large number of cycles (> 105 cycles). These are the high cycle fatigue tests. It should be noted that the stress values plotted are nominal values and does not take into account local stress concentrations It is to be noted that the nominal stress < y, but microscopic plasticity occurs, which leads to the accumulation of damage. As obvious, if the magnitude of Stress increases the fatigue life decreases. Low cycle fatigue (N < 104 or 105 cycles) tests are conducted in controlled derby.ac.u k cycles of elastic + plastic strain (strain control mode, instead of stress 68  Fatigue Broadly two kinds of S-N curves can be differentiated for two classes of materials. (1)Those where a stress below a threshold value gives a ‘very long’ life (this stress value is called the Fatigue Limit / Endurance limit). Steel and Ti come under this category. (2)Those where a decrease in stress increases the fatigue life of the component, but no distinct fatigue life is observed. Al, Mg, Cu come under this category. Thus, fatigue will ultimately occur regardless of the magnitude of the stress. For these materials, the fatigue response is specified as fatigue strength, which is defined as the stress level at which failure will occur for some specified number of cycles. From an application point of view having a sharp fatigue limit is useful (as keeping service stress below this will help with long life (i.e. large number of cycles) for the component). derby.ac.u k 69 Steel, Ti show fatigue limit Al, Mg, Cu show no fatigue limit (Might show a limit, but prohibitive to conduct such long time tests!) derby.ac.u k 70  Impact energy Impact energy: the energy necessary to fracture a standard test piece under an impact load, is a similar analogue of toughness. (a) Charpy test of impact energy. The drop in height between the initial and final pendulum positions ( h) corresponds to the impact energy absorbed by the sample upon fracture. (b) The instant of contact between the Charpy striker (inside the pendulum head) and the sample Image source: Shackelford, J. F. & Shackelford, J. F. (2016) derby.ac.u Introduction to materials science for engineers. 8th ed., Global ed. k Harlow: Pearson Education. 71  Impact energy - For polymers, another type of impact energy test called Izod test is used. derby.ac.u k 72  Impact energy Impact energy is dependent on the geometry of the test sample, chemical composition of the material, temperature and test condition. Impact energy for fcc alloys is generally high over a wide temperature range (ductile failure) Conversely, the impact energy for brittle h c p is generally low over the same range (brittle failure). Ductile to brittle transition temperature (DBTT): bcc metals show dramatic change in impact energy with temperature, they are brittle at low temperatures and ductile at high temperatures. Some examples: low alloys steel. derby.ac.u k 73  Impact energy E(J) 𝐸 h𝑖𝑔h Finding ductile to brittle transition temperature: 1- find the average of energy range: 𝐸 𝑎𝑣𝑒 2- temperature associate with this average energy in the curve is DBTT. 𝐸 𝑙𝑜𝑤 DBTT Temperature ( derby.ac.u k 74