Chapter 5 - Mechanical Properties Flashcards
What are the four key mechanical properties
elastic, plastic, creep, and cracking
What is the effect of neutrons in the primary metal components?
radiation enhanced cracking susceptibility and embrittlement
What are the effects of corrosion in metal components?
crack propagation under stress
What is the pressure balance initially with fuel and water? What does this balance cause?
pressure in coolant is higher than interior causing creepdown of cladding onto pellets
What is the pressure balance towards end of life between fuel and water? What does this cause?
p coolant is less than p interior cladding causing cladding liftoff. This means gap between cladding and fuel increases and fuel overheats since its not being cooled down the same
Why does fuel expand causing pressure increase? What happens with the cladding?
due to fission product swelling which eventually cladding and fuel come into contact again (Gap closure) and continued fuel swelling stresses on cladding.
There are two types of deformation cause by applied load (Stress)?
elastic (removable) or plastics (permanent)
What are the three main sources of stress in nuclear environments?
- Applied external
- Thermal stresses
- residual
What does strain defines?
fractional displacements as a result of applied stress
What are displacements?
changes in the position fo a point as a result of applied stress
What is the diffusion of an atom dependent on in substitutional diffusion?
Upon the presence of a vacancy on an adjacent site and the rate of diffusion therefore depends in how easily vacancies can form in the latice and how easy it is for an atom to move into a vacancy. This dependance upon the presence of vacancies makes substitutional diffusion slower than insterntial diffusion.
Name a candidate material for fast reactors?
HT-9
What metallic component is the first barrier to FP release?
zircaloy
What is the second barrier to FP release?
the primary pressure boundary made of the RPV the coolant piping and the steam generator tubes.
Describe the three steps in fuel cladding interaction throughout lifetime.
Initially the pressure in the coolant is higher than the interior of cladding causing creepdown of cladding onto pellets. Towards the end of life the fission gas release causes pressure to increase in the interior causing cladding liftoff meaning gap increases and fuel overheats. Afterwards, fuel pellets expand due to FP swelling which leads to gap closure and continued fuel swelling causing stress on cladding.
What are the two types of deformation resulting from applied load (Stress)?
elastic (removable) and plastic (permanent).
What is strain?
deformation to a body
What does uniform temperature changes cauases?
thermal expansion but do not generate stresses.
What does non-uniform temperature changes cauases?
thermal stresses and strains
What is the difference between engineering and true stress strain curves?
The engineering stress strain curves assume the cross section remains constant while the true stress strain curves accounts for changes in the cross section area as the experiment precedes.
What is the yield strength?
the stress at which a specific amount of plastic deformation is produced. In other words it indicates the limit of the elastic behaviour meaning the point where deformation is permanent.
What is the elastic modulus?
the quanity that measures an object or substance resisntance to being defomred elastically (non-permanently).
What is the ultimate tensile strenght?
the materials maximum resistance to fracture. It is the maximum engineering stress in a uniaxial stress strain test.
What is the UE
?
What is the TE
?
Where can residual stresses come from?
These are stresses that remain in a solid material after the original cause of the stresses has been removed. Sources include inelastic (plastic) deformation, temperature gradients (during thermal cycle) or structural changes (phase transformation).
What is the difference between strength and toughness?
Strength is the ability of a material to withstand an applied load while toughness is the ability to absorb energy without fracture
What are the three main regions in a UTS graph?
- Elastic
- Stable Plastic (work hardening)
- Unstable Plastic (necking)
What stress is higher: the true or the engineering stress and strain curve?
The true stress-strain curve because the cross sectional area as the experiment proceeds is taken into account meaning A goes down and sigma=P/A=goes up
What does elastic theory relates?
applied loads to non permanent displacements and strains.
How many components does the stress tensor have?
six; three normal and three shear
What does strains define?
The fractional displacements
What is graphed in a UTS?
stress vs strain
What are the three basic components of elasticity theory?
- equilibrium conditions ensuring force balance on a volume element
- displacement and strain relations that ensure the solid remains continuous as it defors
- constitutive equations that related stresses and straines
Elasticity theory applies only for stresses …
less than the yield stress and strain less than a few percent (removable, non-permanent deformation).
What is the youngs modulus?
mechanical property that measures the tensile stiffness of a solid material. It quantifies the relationship between tensile stress and axial strain in the linear elastic region, E = sigma/e where sigma is stress and e is strain. In other words it is the slope of the linear part of the stress strain curve.
What is the poissons ratio?
measures the phenomenon in whic ha material tends to expand in directions perpedincular to the direction of compression.
What is the poisson ratio of rubber and cork? What do they mean?
0.5 and 0 meaning cork has very little compression.
What is the shear modulus?
it is the ratio of shear tress to sheear strain.
What is the youngs or elastic modulus related to fundamentally?
The atomic binding
Does the E-modulus depend on the orientation of the crystal?
Yes
What is stiffness?
the extent at which an object resists deformation in response to an applied force.
What does no texture mean in terms of mechanical properties?
Isotropic mechanical properties meaning same properties in al direction.
What does texture mean in terms of mechanical properties?
anisotropic mechanical properties meaning different properties depending on direction
What does hooks law state?
it states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F = kx where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
How does the thermal expansion coefficients vary with melting temperature
Exponentially go down.
Where do tubes rupture usually? Why
In length axis due to the azimuthal strain
What are the six type of failures in UTS tests?
Type I: Material with no YS Type II: Material with YS Type III: Upper and lower YS Type IV: Ideal plastic behavior Type V: Small Plastic Behavior Type VI: portevin le chatellier effect.
What is hardness?
Is a measure of the resistance of a materials against permanent shape change.
What is elastic deformationin terms of cyrstal planes?
It is the reversible displacement of crystal planes relative to each other. Original structure is recovered when the stress is removed.
What is plastic deformationin terms of cyrstal
is the permanent slippage of crystal planes, which
occurs above a critical stress. When many parallel atomic planes slip relative to each other, macroscopic deformation results
Why is the real critical shear stress many orders of magnitude lower than the theoretical value?
Because of dislocations?
Where will a single cystal plastically deform in a tension test?
The single crystal will plastically deform by shear on
the plane with the highest resolved shear stress.
What does the schmid factor describe?
The Schmid factor describes the relationship between external normal stresses and the shear stresses caused in a slip system!
What is the relationship between youngs modulus and melting temperature?
Melting temperature is also an indicator of atomic bonding strength and there is relationship with Young’s modulus. The general trend is that a higher melting temperature indicates a higher modulus and vice versa.
What is the relationship between the youngs modulus and the thermal expansion?
Young’s modulus, aka elastic modulus is more or less the stiffness of a material. In rough terms, it is the change in stress caused or divided by a change in strain. The bigger the modulus, the stiffer the material.
Coefficient of thermal expansion is the change in strain caused by a change in temperature. The two concepts tend to be inverse.
Why do some stress strain cruves show a peak at yielding?
A point at which Maximum load or stress required to initiate the plastic deformation of material such point is called as Upper yield point. And a point at which minimum load or stress required to maintain the plastic behavior of material such a point is called as Lower yield point.
Why is schmid law important and what are the implications for a polycrystalline material?
Since there is no define slip system due to the random orientation of grains in the pollycristalline system then it isusually stronger than signle crystals.
The crystal with the largest resolved shear stress (Tr) yields first and others later.
What is the hall petch relationship?
The Hall–Petch relationship tells us that we could achieve strength in materials that is as high as their own theoretical strength by reducing grain size.
What are lueders band attributed to?
Impurities like carbon and nitrogen can pint dislocations leading to an upper yield point. Once dislocations break loose from pinning points they start moving but still encountering pinning pints.
What are the four main failiure modes?
Ductile, Brittle, Fatigue, Creep
Describe ductile failiure. What does the stress strain grpah look like?
Necking, formation of pores at impurities/inclusions, joining of small pores to a crack, and final rupture at the highest shear stress in an angle (max shear stress).
smooth
Describe brittle failiure. What does the stress strain grpah look like?
Initial dislocation motion, moving dislocations fruther costs more energy than nucleating a crack, brittle fracture-cracking. Dislocations start to pile up.
sudden break withouth the plastic section.
What other tests is used for brittle materials since these cannot be tested easy in tension?
Compression tests.
What is fatigue?
weakening of am aterial caused by cyclic loading that results in progressive and localized structural damage and the growth of cracks. Once a fatigue crack has initiated, it will grow a small amount with each loading cycle, typically producing striations on some parts of the fracture surface.
What is strain aging?
When steel has been strained (deformed plastically) and then allowed to age, it has been subjected to what is known as strain ageing
What is aging?
Aging is an essential step that ensures that the materials in the alloy do not revert to their original configuration after a time period. Aging is performed under controlled conditions so that the resultant grain structure will create a greater tensile strength in the metal than in its former state.
Describe the le chattelier dislocation process.
In materials, the motion of dislocations is a discontinuous process. When dislocations meet obstacles during plastic deformation (such as particles or forest dislocations), they are temporarily arrested for a certain time. During this time, solutes (such as interstitial particles or substitutional impurities) diffuse around the pinned dislocations, further strengthening the obstacles’ hold on the dislocations. Eventually these dislocations will overcome the obstacles with sufficient stress and will quickly move to the next obstacle where they are stopped and the process can repeat
What is dynamic strain aging?
Dynamic strain aging (DSA) is a process where aging is sufficiently rapid to occur during straining and it produces a variety of inhomogeneous deformations which are characterized by terms such as Portevin-le Chatelier effect, serrated yielding, jerky or serrated flow, blue brittleness, etc.
How are the related graphs called displaying the materials lifetime? What are the two axis?
wohler diagram plots the stress and the number of cycles to failure
What is creep?
Creep is a time (also stress and temperature) dependent mechanical deformation of solids which occurs slowly at stresses below the ultimate tensile
stress. The time dependence differentiates creep from plastic deformation.
Can dislocations climb?
Yes, they can climb due to the vacancy movement and this allows dislocations to climb over obstacles.
What is coble creep?
A form of diffusion creep in which atoms migrate along grain boundaries
What is diffusion creep?
refers to the deformation of crystalline solids by the diffusion of vacancies through their crystal lattice. Diffusion creep results in plastic deformation rather than brittle failure of the material.
Explain diffusion creep.
Diffusion creep is caused by the migration of crystalline defects through the lattice of a crystal such that when a crystal is subjected to a greater degree of compression in one direction relative to another, defects migrate to the crystal faces along the direction of compression, causing a net mass transfer that shortens the crystal in the direction of maximum compression. The migration of defects is in part due to vacancies, whose migration is equal to a net mass transport in the opposite direction.
What is the nabarro herring creep?
is a mode of deformation of crystalline materials (and amorphous materials) that occurs at low stresses and held at elevated temperatures in fine-grained materials. In Nabarro–Herring creep (NH creep), atoms diffuse through the crystals, and the creep rate varies inversely with the square of the grain size so fine-grained materials creep faster than coarser-grained ones.
What does creep depend on?
Time, temperature, stress
What is the larson miller parameter?
is a means of predicting the lifetime of material vs. time and temperature using a correlative approach based on the Arrhenius rate equation
What is a requirement for superplasticity?
grain size since grain boundary sliding and grain rotation is resposible for this phehonema due to diffusion at grain boundaries.
What is the charpy impact test?
is a standardized high strain-rate test which determines the amount of energy absorbed by a material during fracture. Absorbed energy is a measure of the material’s notch toughness. The qualitative results of the impact test can be used to determine the ductility of a material. If the material breaks on a flat plane, the fracture was brittle, and if the material breaks with jagged edges or shear lips, then the fracture was ductile. Usually, a material does not break in just one way or the other and thus comparing the jagged to flat surface areas of the fracture will give an estimate of the percentage of ductile and brittle fracture
Are typical real condition uniaxial as tests?
No, they are uniaxial.
What is the von mises criterion?
The von Mises stress is used to predict yielding of materials under complex loading from the results of uniaxial tensile tests.
Is the temperature in the fuel pellet uniform?
No, there is a gradient from center line to surface.
What happens when tensile stresses excieed critical value for ductile and brittle materials?
Macrooscopic plasticity or cracking
What orientation are cracks in fuel pellets and why?
Radiallly oriented (perpendicular to the angle direction, perpendicular to the cladding surface point) since the sstress going outwards is higher than the stress going on height.
What is strain?
is defined as the change in dimensions of a material (based on the original dimensions) as a result of an applied stress.
What is the main source of strain in the cladding causing deformation?
Strains induced by pellet thermal expansion.
What is the pellet shape after deformation due to strains?
Hour-glassed
How do we measure the ability of a material to withstand thermal stresses?
ratio of thermal stress to failure stress where failure is either fracture for ceramics or yielding for ductile metals.
What is the thermal stress parameter?
a parameter that mesaures the resisntace to thermal stress failiure which is a function of the failiure stress (yield or fracture), the thermal conductivity and the thermal expansion coeffcieitn. The larger the more thermal stress resistant
What makesa material a good thermal stress failure resistance?
Large failure stress, high thermal conductivity and l ow thermal expansion coefficient
What is the stress? What units are used?
force applied per unit area, typically measured in 𝑀𝑃𝑎=106 𝑁/𝑚2:
What is the formula for stress?
stress (sigma) = F/A
where:
F = the force applied normal to the sample’s cross-sectional area
A = the cross-sectional area of the sample
What is the strain? What units are used?
sample displacement per unit length, unitless (often quoted as %)
What is the formula for strain?
e = deltaL/L
where L is the length and deltaL is the change in length.
What is tension?
positive strain
What is compression
negative strain
What is elastic deformation?
completely recoverable deformation where the body returns to its original shape once the external forces are removed. Atomic bonds are stretched, but not broken.
What is the relationship between stress and strain in elastic deformation? formula?
linear, hookes law
stress (sigma) = E*strain where E is the youngs modulus/elastic modulus
How is the youngs modulus determined?
by the interatomic forces in the material, and is dependent on crystal structure and orientation in the material, however it is not very affected by alloying, cold working, or heat treatment.
How does the youngs modulus behave with temperature
The Young’s modulus does decrease with increasing temperature as the interatomic forces become weaker.
What is the poisons ratio?
When a material is stretched in one direction, it tends to contract in the other two directions (or vice versa for compression). This relationship is captured with Poisson’s ratio, 𝜈.
What is the formula for the poisons ratio
v = - strain on x / strain on z if pulled on the z direction
What is the plastic deformation?
permanent deformation, which does not recover once the forces are removed.
How is plastic deformation accomplished?
through dislocation motion which facilitates the slipping of lattice planes against one another
What is tensile testing?
popular method of studying short-term mechanical behavior (strength and ductility) of a material. The test is performed with a quasi-static uniaxial tensile stress state (the sample is being stretched along one direction at a sufficiently slow and usually constant rate – aka, no sudden changes)
What is the issuw with the engineering stress and strain?
does not take into account the fact that the cross sectional area and length of the specimen are not constant throughout the test.
What are the four different regimes of material behaviour?
- elastic regime
- yield point
- plastic regime (uniform strain)
- plastic regime (nonuniform strain)
What is the elastic regime in a stress vs strain curve
the initial linear regime of the curve where the material experiences elastic deformation only.
What is the slope of the elastic regime equivalent to?
Youngs modulus
What is the yield point?
The point where the deformation is nonlinear. In other words is marks the transition from elastic to plastic deformation. The yield points value is the yield stress
What is the plastic regime (uniform strain)?
where plastic deformation occurs also reffered to as strain hardening regime. Here, the cross sectional area decreases in a uniform manner and ocntinues until it reaches a maximum aat the Ultimate Tensile Strength (UTS).
What does the UTS make?
The transition between uniform and non uniform plastic deformation. It also marks the point where necking occurs.
Why are sometimes upper and lower yield points?
This occurs when dislocation movement gets impeded by interstitial atoms such as carbon, nitrogen, and so on forming solute atmospheres around the dislocations. However, at very high stress, the dislocations break away from the solutes and thus require less stress to move at this point.
What is the yield point elongation?
The elongation that occurs at constant load or stress at the lower yield point
What are luders bands?
During yield point elongation, a type of deformation bands known as “Lüders bands” are formed across the yield elongation regime
What happens after the luders bands?
After the Lüders bands cover the whole gauge length of the specimen, the usual strain hardening regime sets in.
What is the difference between the true and engineering stress vs strain
true stress strain takes into account the change in cross sectional area and length as the experiment carries on.
What is the difference between the true and engineering stress vs strain in terms of how ithe curve looks?
the true stress to continue increasing past necking as the test is continued. meaning the true curve is higher and the fracture usually happens with more strain.
Why, if the load does not increase pass neckign in a true stress vs strain curve, the true stress continues to increasing?
due to the decreased cross sectional area that is now being put in tension.
How does the brittle stress strain curve look in comparison to the ductile stress strain?
The brittle has a steeper elastic regime and a higher fracture point but all happening at much less strain
In terms of the the tensile test rod, how does the brittle, ductile fracture, and ductile fracture in polycrystallines look like?
- Square like sudden break
- elongated diagonal break
- pen-like and middle flaw
What is ductility?
is a measure of the degree of plastic deformation that can be sustained at fracture.
What is a brittle material?
has very low ductility, meaning it tends to fracture at low strains after little plastic deformation. Brittle materials are considered to be those with a fracture strain of
What are the three main equations and ocnditions of elasticity theory?
- equilibrium conditions
- relations between displacements and strains
- constitutive equations
What is the von misses model?
method to determine which combination of stress components is equivalent to a uniaxial stress
What is the azimuthal force?
It is the PR/tt
pressure * tube radius/tube thickness
Which is higher and by how much? the azimutal or the axial force?
the azimuthal force is two times larger than the axial force
Why do tubes rupture sausgae like?
Because the azimuthal force is 2 times larger than the axial force.
What is the azimuthal strain a functio of?
The azimuthal force the normal force, the reference temperature and the thermal expansion coefficient
What is texture?
he distribution of crystallographic orientations in a polycrystalline material.
no texture = the orientations are fully random, there is no preferred orientation
strong texture = material has a preferred orientation
How do you measure texture?
with X-ray diffraction, EBSD (electron backscatter diffraction) in an SEM (scanning electron microscope), and other diffraction techniques
What is the effect of rolling metal?
Textrue introduction and elongated grains along the rolling direction resulting in direciton dependent properties
What is hardness?
resistance to indentation
Why is hardness testing useful?
characterize mechanical properties in materials, particularly the resistance to deformation.
It does not involve total destruction of the sample as needed in tensile testing, and generally requires only a small volume of material.
Is hardness the same as strenght?
Hardness is not the same as strength, however hardness values are generally proportional to the strength values obtained in tension or compression tests.
Why are dislocations ipmortant to strengthenigna nd hardening mechanisms?
If dislocations are able to move in a crystal with relative ease, it means the material does not intrinsically offer any resistance to the dislocation movement and thus would be less strong. But if the microstructure is laden with various obstacles, dislocation movement will be effectively impeded and this movement obstruction will be translated into an increase in strength.
What can act as dislocations obstacles?
Obstacles to dislocations can be dislocations themselves (strain hardening), grain boundaries (Hall-Petch and grain size strengthening), solute atoms (solid solution strengthening), precipitates (precipitation strengthening), and dispersions of fine stable particles (dispersion strengthening).
What is strain hardening?
The hardneing of a material by the introduction of dislocations. When a metal is cold-worked, its strength increases. As dislocation density is increased, the movement of dislocations becomes increasingly difficult due to the interfering effect of the stress fields of other dislocations. In the early stages of plastic deformation, slip is generally limited on primary glide planes and the dislocations tend to form coplanar arrays. However, as the deformation proceeds, cross-slip takes place and dislocation multiplication mechanisms start to operate. The cold worked structure then forms high dislocation density regions or tangles that soon develop tangled networks
What is the density of dislocatiosn in annealed compared to cold worked?
annealed crystal contains a dislocation density of about 10E8 m−2. Heavily cold worked materials may contain 10E14 to 10E16 m−2.
What is grain size strengthening?
Grain boundaries can act as obstacles to dislocation motion. As grain orientation changes at the grain boundary, slip planes in a grain get disrupted at the grain boundary. Thus the dislocations gliding on a slip plane cannot burst through the grain boundary. Instead, they get piled up against it therefore limiting dislocation movement and causing hardening.
What is the effect of grain size in grain size strengthening?
A greater stress concentration is created at a larger grain, which has enough energy to push through to the next grain. For smaller grains, the stress concentration is not great enough to produce slip in the next grain readily, thus fine grained materials exhibit higher yield strength.
What is the hall and petch equation?
mathematical relationship between yield stress and grain size whic his a fucntio of the friction stress or yield strengh at infinite grain size and the unlocking parameter which measures relative hardenign contributio of grain boudaries and the grain diameter.
What is solid solution strengthening?
Dislocations encounter barriers on their path from the solutes present in the host lattice.
What is precipitation hardening?
Dispersed particles impart significant obstacles on dislocation motion. When the particles are small (<5 nm), and/or soft and coherent, dislocations can cut and deform the particles (“particle shearing”). For larger precipitates, the phenomenon of Orowan bypassing occurs, in which the dislocations form loops around the particles.
What is orowan bypassing?
in which the dislocations form loops around the particles.
What is the size limit for particle shearing
less than 5 nm
What is particle shearing?
When the particles are small (<5 nm), and/or soft and coherent, dislocations can cut and deform the particles (“particle shearing”).
What are impact tests?
are used to measure the resistance to failure of a material under a sudden applied force. They are intended to study the most severe conditions relative to the potential of fracture
What do impact tests measure?
Impact tests measure the impact energy, or the energy absorbed prior to failure.
What is the stress intensity factor, K? What does it depend on?
The elastic stress field around a crack tip
it depends on the geometry of the crack-containing solids, the size and location of the crack, and the magnitude and distribution of the loads applied.
What happens if the stress intensity factor K is surpassed?
Rapid unstable failure
What are the three cracking modes?
- Opening mode displacement perpendicular to crack faces
- displacement parallel to crack faces but perpendicular to the edge
- tearing mode parallel to the crack faces and to the leading edge
What is the plain strain fracture toughness? What does it depend on?
The critical stress intensity factor Kic
Kic = Ysigmasqrt(pi*ac)
It depends on the specimen and crack geometry, the applied stress (sigma), and the critical crack length (ac).
If Kic is known, this can be used to compute the _____ tolerable
the maximum crack length
In what scenarios is considering treep important?
In load bearing structure exposed to elevated temperatures for a long duration of time.
What is creep?
Time dpeendent plastic strain at constant temperature and stress
When does creep occurr?
above half the melting temperature.
What is the creep test?
A creep test is generally done under uniaxial tensile stress. A creep curve is plotted as creep strain vs. time at a constant load and temperature
What are the three stages in a creep test curve?
- Primary stage (transient creep)
- secondary or second stage creep (minimum creep rate)
- tertiary stage
What are the two competing factors in the creep test curve?
- the strain hardening tthat occurs when something is plastically deformed due to dislocations getting tangled in each other.
- softening that occurs as a result of the creep which causes easy plastic deformation to occur.
What is happening in the primary stage of the creep test curve?
In the first stage work hardening during plastic deformation rules over recovery/softening mechanisms therefore exhibiting decreasing strain rate with time.
What is dislocation hardening?
This strengthening occurs because of dislocation movements and dislocation generation within the crystal structure of the material.
What are the three creep mechanisms?
- dislocation creep
- nabarro=herring creep
- coble creep
What is the dislocation creep mechanism?
At high stresses, creep is controlled by dislocation motion. This is accomplished by both dislocation glide and climb, however climb is the rate-controlling element in creep. The glide motion of dislocations is impeded by long range stresses due to dislocation interactions. These stresses can be relieved by dislocation climb and subsequent annihilation.
What is the nabarro herring creep mechanism?
Creep due to the diffusion of vacancies through the lattice (through grains)
What is the coble creep mechanism?
Creep due to the diffusion of vacancies along grain boundaries.
Why does irraidation enhance creep?
Because creep mechanisms like nabarro herring and coble creep mechanisms depend on the diffusion of vacancies. Vacancy concentration increases with irradiation.
How do you activate nabarro herring creep?
With high temperatures sinc eit requires energy to transprot vacancies through grains than along grain boundaries. Irradiation can help.
What is fatigue?
weakening of a material caused by repeated applied loads (cyclic loading)
What is an S-N curve?
If the stress amplitude (S) is plotted against the number of cycles to failure (N). It represents the number of cycles needed for failiure given a stress.
What is a fatigue limit?
For some ferrous materials and titanium alloys, the S-N curve becomes horizontal at higher N values, or there is a limiting stress level called the “fatigue limit” or “endurance limit”, which is the largest value of fluctuating stress that will not cause failure for essentially an infinite number of cycles.
How does an SN curve ususally look l ike
As the stress increases the number of cycles decreases. As the stress decreases the number of cicles increases.
