MILL Wiki - User contributions [en]

Thermo-Calc

2021-08-08T10:00:02Z

Akulaksizoglu3:

[[File:Thermo Calc Logo.png|thumb|Thermo-Calc is available to all MSE students.]]

=== Why Use Thermo-Calc? ===
Thermo-Calc is primarily used to calculate the state for a given thermodynamic system, predict a wide range of materials property data, and gain insight into materials processing. Visit [https://thermocalc.com Thermo-Calc's Website] for more information.

=== '''How to Download Thermo-Calc?''' ===
To download Thermo-Calc 2021B edition, visit http://msedb.gatech.edu/TCalc/ and download the appropriate installer file depending upon your operating system. To get the files you will be asked for a username and password. They are:

''user - TC''

''pw - Thermo5C''

There is also a multi-OS Installation Guide available in the download section, but it is not likely needed for the typical Windows installation.

This instruction below relates to a '''Windows''' installation. If you are doing an '''OSX''' install, you must first install Apple's free XQuartz software in order to have Thermo-Calc function.

The install you will be doing is the *Typical Network Client* install, not the Standalone nor Custom. There is no license file with these downloads, as each install communicates with an existing license server.

As soon as you select the Typical Network Client install you will be asked for the IP address of the license server, which is:

''128.61.136.120''

If you are given the option to select that the software be useable by "Current User" or "All Users" on the system, generally, "All Users" would be the best selection.

Three modules are installed and integrated into program by default, Thermo-Calc, Diffusion Simulation (DICTRA), and Precipitation Simulation. The Thermo-Calc icon is placed on the desktop by default.

Once the install is finished, run Thermo-Calc and it should come up if it can communicate with the license server. Our firewall is prepared to accept the inquiry from other campus subnets.

The databases that are available to the Thermo-Calc program are determined by the license file that resides on the license server.

==== Installation Problems Observed ====
The Windows installation has been done in Windows 7 and Windows 10, 64-bit. On some machines, particularly those that may have had Thermo-Calc before, two problems have been observed.

If you try to uninstall an old version of Thermo-Calc you may run into a Windows error related to missing Java components. Per Thermo-Calc, there is no need to remove an old version, as they do not interfere.

Plus, these system may have an unexpected reboot just as the installation finish is approached. Upon restart, you will have to again run the installer just as before. When it reports "files from existing installation detected, Install anyway?" you respond with "yes" and installation will run to normal completion.

Thermo-Calc

2021-08-08T09:52:15Z

Akulaksizoglu3:

[[File:Thermo Calc Logo.png|thumb|Thermo-Calc is available to all MSE students.]]

Thermo-Calc

2021-08-08T09:50:13Z

Akulaksizoglu3: Created page with "a"

Index.php?title=Thermo-Calc

2021-08-08T09:49:08Z

Akulaksizoglu3: Created page with "s"

Category:Software

2021-08-08T09:47:27Z

Akulaksizoglu3: /* General */

List of distributable software from the MILL and software available to all GT students.

== General ==
* MATLAB
* Origin
* AutoCAD
* SolidWorks
* CES EduPack
* [[COMSOL Multiphysics]]
*[[Index.php?title=Thermo-Calc|Thermo-Calc]]

== Characterization ==
* PhenomImageViewer ([[Scanning Electron Microscope (SEM)|SEM]])
* CrystalMaker Suite ([[X-ray Diffractometer (XRD)|XRD]])
** CrystalMaker
** CrystalDiffract
** SingleCrystal
* Jade Pro ([[X-ray Diffractometer (XRD)|XRD]])

== Measurement ==
* n/a

== Processing ==
* Ultimaker Cura
* PrusaSlicer

File:Thermo Calc Logo.png

2021-08-08T09:43:46Z

Akulaksizoglu3:

Thermo Calc Logo

COMSOL Multiphysics

2021-08-08T09:39:21Z

Akulaksizoglu3: Created page with "=== Why Use COMSOL? === COMSOL Academic Class Kit is available to all GT students. COMSOL is primarily used to simulate designs, devices, and pr..."

=== Why Use COMSOL? ===
[[File:Comsol Logo.png|thumb|COMSOL Academic Class Kit is available to all GT students.]]
COMSOL is primarily used to simulate designs, devices, and processes in all fields of engineering, manufacturing and scientific research. Check out [https://www.comsol.com/blogs/10-real-uses-of-comsol-multiphysics-in-the-power-industry/ this article] by COMSOL to see real life examples of COMSOL's industrial use.

==== MSE Applications of Comsol ====
COMSOL's Material library contains more than 30,000 property functions. It specifies various properties of over 3800 materials. This makes it ideal for multiphysics couplings such as electrical thermal analysis, structural-thermal analysis, because most of the properties are available as functions of temperature. COMSOL also has Battery design, Electrochemistry, Electrodeposition, Fatigue, Fuel Cell & Electrolyzer, Heat Transfer, Liquid and Gas properties, Metal processing, Particle tracing, Polymer flow, Polymer media flow, Porous media flow, Semiconductor, Structural mechanics modules.

=== How to Access COMSOL? ===
GT provides virtual access to COMSOL through its Academic ClassKit License. To use COMSOL, log onto https://mycloud.gatech.edu/vpn/index.html with your credentials, select COE 2021 when asked to choose a computer. COMSOL's Academic Class Kit along with [https://doc.comsol.com/5.6/docserver/#!/com.comsol.help.comsol/helpdesk/helpdesk.html COMSOL's documentation] will be available to you when you log in.

File:Comsol Logo.png

2021-08-08T09:22:37Z

Akulaksizoglu3:

Comsol Logo

Category:Software

2021-08-08T09:18:06Z

Akulaksizoglu3: /* General */

List of distributable software from the MILL and software available to all GT students.

== General ==
* MATLAB
* Origin
* AutoCAD
* SolidWorks
* CES EduPack
* [[COMSOL Multiphysics]]
*[[ThermoCalc]]

== Characterization ==
* PhenomImageViewer ([[Scanning Electron Microscope (SEM)|SEM]])
* CrystalMaker Suite ([[X-ray Diffractometer (XRD)|XRD]])
** CrystalMaker
** CrystalDiffract
** SingleCrystal
* Jade Pro ([[X-ray Diffractometer (XRD)|XRD]])

== Measurement ==
* n/a

== Processing ==
* Ultimaker Cura
* PrusaSlicer

Mechanical Testing

2021-06-28T16:54:00Z

Akulaksizoglu3: corrected a typo

{|class="infobox"
!style="font-size:135%;text-align:center;" | Mark-10 ESM303
!style="font-size:135%;text-align:center;" | Instron 5967
|-
|[[File:Mark10-052621.png|center|250px]]||[[File:Instron-052621.png|center|250px]]
|-
|'''Load Cells''': 500 mN, 25N, 500N, 1500N||'''Maximum Force''': 30kN
|}

The Mark-10 ESM303 Mechanical Tester is a mechanical testing frame capable of testing materials under tensile, cyclic, compressive, and 3-point bending modes. This machine has several load cells: a 1500 N, a 500 N, a 25 N, and a 500 mN load cell.

The Instron Mechanical Tester is a mechanical testing frame capable of testing materials under tensile, compressive, and 3-point-bending modes. This machine is equipped with a 30kN load cell.

== Loading ==
[[File:Loading.PNG|thumb|350px|left|1. Compression 2. Tension 3. Shear 4. Torsion 5. Bending]]

A material in service is subjected to different forces. Depending on the magnitude of these forces, the metal may or may not change its shape. The act of applying the force is known as loading. There are several different ways in which these forces may be applied on a part, including compression, tension, and bending. <ref name="Velling"> Velling, A. (2021, May 5). Stress-Strain Curve: How to Read the Graph? Fractory. https://fractory.com/stress-strain-curve/. </ref> <ref name="Meyers">Meyers, M., & Chawla, K. (2016). Hardness. In Mechanical Behavior of Materials (2nd ed., pp. 214–225). chapter, Cambridge University Press.</ref>

== Stress and Strain ==
Stress is defined as the ratio of applied force to the cross-sectional area of the material it is applied to. The formula for calculating (true) material stress is:

<math> \sigma_t =\frac{F}{A}, </math>

Where ''F'' is force, ''A'' is area, and <math> \sigma </math> is stress. Stress can be understood as an internal force induced in the material in response to an externally applied force (Newton’s 3rd law). It will try to resist any change in dimension caused by the external force. Strain is defined as the ratio of the change in dimension to the initial dimension of the metal. It does not have a unit (sometimes designated as length/length). The formula for calculating (true) strain is:

<math> \epsilon_t = \int_{l_0} ^l \frac{dl}{l} = ln(\frac{l}{l_0}), </math>

Where <math> l_0 </math> is starting or initial length, ''l'' is current length, and <math> \epsilon </math> is strain. In many applications, a simpler form of strain, commonly called engineering or nominal strain, is used. This type of strain is defined as

<math> \epsilon_e = \frac{(l-l_0)}{l_0} </math>

When the strains are reasonably small, the engineering and true strains are approximately the same. The elastic deformation in metals and ceramics rarely exceeds 0.005, and for this value, the difference between <math> \epsilon_t </math> and <math> \epsilon_e </math> can be neglected. In a likewise fashion, engineering (nominal) stress is defined as:[[File:SScurve.PNG|thumb|Engineering stress-strain curve of a typical ductile material <ref name="Roylance"> Roylance, D. (2001, August 23). STRESS-STRAIN CURVES.</ref>]] <math> \sigma_e = \frac{F}{A_0} </math>

where <math> A_0 </math> is the original area of cross-section. Normal strain may be positive or negative depending on the external force’s directions and therefore effect on the original length. Tensile stresses and strains are considered to be positive while their compressive counterparts are considered to be negatives. While there are multiple types of stresses and strains, this article focuses on their normal longitudinal variants.

== Tensile Testing & Engineering Stress-Strain Curves ==
The most common method to obtain a stress-strain curve is to subject a sample to a tensile test. When setup for tensile testing, the mechanical testers have two claws which hold the two extremes of the sample and pull it at a uniform rate. The force applied and the strain produced is recorded until a fracture occurs. The two parameters are then plotted on an X-Y graph to get a stress-strain curve. Note that the testers produces a force-travel plot (with the same general shape) that must be manually converted to a stress-strain curve using the aforementioned equations in conjunction with the sample dimensions (or entering the sample dimensions into the software on the Instron). There are various sections on the stress and strain curve (described below) that describe different behavior of a material depending on the amount of stress induced. Stress and strain curves for brittle and ductile materials are different.

[[File:BrittleSSCurve.PNG|thumb|300x300px|Typical stress-strain curve of a brittle material <ref name="MechaniCalc> "Mechanical Properties of Materials. MechaniCalc. (n.d.). https://mechanicalc.com/reference/mechanical-properties-of-materials.</ref>]]

== Elastic & Plastic Deformation ==
In the early (low strain) portion of the curve, most materials obey Hooke’s Law <math> (F_s=kx) </math> to a reasonable approximation, with the constant of proportionality being the modulus of elasticity or Young’s modulus (E), described by the following equation:

<math> \sigma_e = E\epsilon_e \rightarrow E= \frac{\sigma_e}{\epsilon_e} </math>

Also known as the modulus of resilience, it is analogous to the stiffness of a spring (''k''). That’s also why Hooke’s Law includes a spring constant. Materials exhibit elastic flow (ability to return to their original shape upon unloading) up to a certain strain.

As strain is increased, many materials eventually deviate from the linear proportionality of Hooke’s Law, the point of departure being termed the proportional limit. This is usually associated with stress-induced “plastic” flow in the specimen. Here the material is undergoing a rearrangement of its internal molecular or microscopic structure, in which atoms are being moved to new equilibrium positions. This plasticity requires a mechanism for molecular mobility, which in crystalline materials can arise from dislocation motion. Materials lacking this mobility, for instance by having internal microstructures that block dislocation motion, are usually brittle rather than ductile (fail at lower rather than higher strains). The stress-strain curve for brittle materials are typically linear over their full range of strain, eventually terminating in fracture with no to minimal plastic flow (permanent deformation).

== Yield Stress ==
[[File:0.2Offset.PNG|thumb|Graphical depiction of finding 0.2% offset yield strength (stress)]]
The stress needed to increase the strain beyond the proportional limit in a ductile material continues to rise beyond the proportional limit; the material requires an ever-increasing stress to continue straining, a mechanism termed strain hardening. Microstructural rearrangements associated with plastic flow are usually not reversed. The residual strain induced by a given stress can be determined by drawing an unloading line from the highest point reached on the engineering stress strain curve at that stress back to the strain axis, drawn with a slope equal to that of the initial elastic loading line. This is done because the material unloads elastically, there being no force driving the molecular structure back to its original position. A closely related term is the yield stress <math> (\sigma_y) </math>; this is the stress needed to induce plastic deformation in the specimen. Since it is often difficult to pinpoint the exact stress at which plastic deformation begins, the yield stress is often taken to be the stress needed to induce a specified amount of permanent strain, typically 0.2%. The construction used to find this “offset yield stress” is shown below, where a line of slope E is drawn from the strain axis at <math> \epsilon = 0.2\% </math>; this is the unloading line that would result in the specified permanent strain. The stress at the point of intersection with the curve is the offset yield stress. Engineering calculations typically use a material’s yield strength for determining its ability to resist a load because if the load is greater than the yield strength, the result will be unwanted plastic deformation. See [https://www.youtube.com/watch?v=p0TQ8SV0g2U&t=586s this video] for a detailed explanation of how to find the 0.2% offset yield stress & strain in Excel.

== Ultimate Strength ==
It appears that the rate of strain hardening decreases up to the ultimate strength (UTS), the greatest level of stress on the curve. Beyond that point, the material appears to strain soften, so that each increment of additional strain requires a smaller stress. The apparent change from strain hardening to strain softening is an artifact of the plotting procedure (using engineering rather than true values), as is the maximum observed in the curve at the UTS. Even though the UTS is perhaps the materials property most commonly reported in tensile tests, it is not a direct measure of the material due to the influence of geometry, and should be used with caution. The yield stress is usually preferred to the UTS in designing with ductile metals, although the UTS is a valid design criterion for brittle materials that do not exhibit flow-induced reductions in cross-sectional area.

== Necking ==
[[File:Necking.PNG|thumb|Necking in a tensile specimen]]
The true stress is not quite uniform throughout the specimen, and there will always be some location - perhaps a nick or some other defect at the surface - where the local stress is maximum. Once the maximum in the engineering curve has been reached, the localized flow at this site cannot be compensated by further strain hardening, so the area there is reduced further. This increases the local stress even more, which accelerates the flow further. This localized and increasing flow soon leads to a “neck” in the gage length of the specimen such as that seen below.

Until the neck forms, the deformation is essentially uniform throughout the specimen, but after necking all subsequent deformation takes place in the neck. The neck becomes smaller and smaller, local true stress increases all the time, until the specimen fails. This will be the failure mode for most ductile metals. As the neck shrinks, the nonuniform geometry there alters the uniaxial stress state to a complex one involving shear components as well as normal stresses.

== Drawing ==
[[File:Drawing.PNG|thumb|Necking and drawing in a stress-strain curve]]
This figure shows the engineering stress-strain curve for a semi-crystalline thermoplastic. The response of this material is similar to that of typical metals, in that it shows a proportional limit followed by a maximum in the curve at which necking takes place. (This is commonly described in plastics as the yield stress, although plastic flow has begun at earlier strains.) The polymer, however, differs dramatically in that the neck does not continue shrinking until the specimen fails. Rather, the material in the neck stretches only to a “natural draw ratio” which is a function of temperature and specimen processing, beyond which the material in the neck stops stretching and new material at the neck shoulders necks down. The neck then propagates until it spans the full gage length of the specimen, a process called drawing. This process can be observed without the need for a testing machine, by stretching a “six-pack holder.” Not all polymers are able to sustain this drawing process. Drawing occurs when the necking process produces a strengthened microstructure whose breaking load is greater than that needed to induce necking in the untransformed material just outside the neck.

== Failure ==
[[File:BrittleDuctile.PNG|thumb|Smooth brittle fracture (left) and "cup and cone" shaped ductile fracture (right)]]
Ductile specimens often fail with a “cup and cone” geometry as seen below, in which the outer regions fail in shear and the interior in tension. When the specimen fractures, the engineering strain at break <math> (\epsilon_f) </math> will include the deformation in the necked region and the un-necked region together. Since the true strain in the neck is larger than that in the un-necked material, the value of <math> (\epsilon_f) </math> will depend on the fraction of the gage length that has necked. Therefore, <math> (\epsilon_f) </math> is a function of the specimen geometry as well as the material, and thus is only a crude measure of material ductility. Brittle specimen failure is characterized by very rapid cracking under stress while little or no evidence of ductility or plastic degradation before the fracture occurs. When a piece of equipment suffers a brittle fracture, there is no thinning or necking down. Rather, this damage mechanism often causes cracking without warning, sometimes fracturing equipment into many pieces. Brittle fracture is often caused by low temperatures. If a metal is at or below its brittle-to-ductile transition temperature, then it will be susceptible to brittle fracture. Critical sized flaws, metallurgical degradation, large grain sizes, and high thickness significantly increase the likelihood of a sample experiencing brittle fracture.

== True Stress-Strain Curve ==
[[File:TrueSSC.PNG|thumb|A true stress-strain curve compared its engineering counterpart <ref name="fracture"> United States Naval Academy. (n.d.). FRACTURE OF MATERIALS. </ref> ]]
During elastic deformation, the change in cross-sectional area is less than 1% for most metals and ceramics; thus <math> \sigma_e ∼= \sigma_t </math>. However, during plastic deformation, the differences between the true and the engineering values become progressively larger as the specimen dimensions experience substantial change from their original values. Due to this, the engineering stress-strain curve must be interpreted with caution beyond the elastic limits. Using the true stress <math> \sigma_t = \frac{F}{A} </math> rather than the engineering stress <math> \sigma_e = \frac{F}{A_0} </math> can give a more direct measure of the material’s response in the plastic flow range, although this requires using the following additional equations:

<math> \epsilon_t =ln(1+\epsilon_e) </math>
<math> \sigma_t = \sigma_e(1+\epsilon_e) </math>

Ductile metals often have true stress-strain relations that can be described by a simple power-law relation of the form:

<math> \sigma_t = A\epsilon_tn → log(\sigma_t) = log(A) + nlog(\epsilon_t) </math>

The strain hardening parameter (n), is the slope of the log-log plot, and is useful as a measure of the resistance to necking. Ductile metals at room temperature usually exhibit values of n from 0.02 to 0.5.
[[File:Toughness.PNG|thumb|Resilience and toughness shown graphically]]

== Strain Energy, Resilience, & Toughness ==
[[File:EnergyDissipated.PNG|thumb|How to graphically determine energy dissipated in a plastically deformed (but not fractured) specimen ]]
The area under the engineering stress-strain curve up to a given value of strain is the total mechanical energy per unit volume consumed by the material in straining it to that value. This is easily shown as follows:

<math> U^* = \frac {1}{V} \int FdL= \int_0^L \frac{FdL}{A_0L_0}= \int_0^{\epsilon}\sigma d\epsilon </math>

In the absence of molecular slip and other mechanisms for energy dissipation, this mechanical energy is stored reversibly within the material as strain energy. The area up to the yield point is termed the modulus of resilience, and the total area up to fracture is termed the modulus of toughness.

The term “resilience” alludes to the concept that up to the point of yielding, the material is unaffected by the applied stress and upon unloading will return to its original shape. But when the strain exceeds the yield point, the material is deformed irreversibly, so that some residual strain will persist even after unloading. The modulus of resilience is then the quantity of energy the material can absorb without suffering damage. Similarly, the modulus of toughness is the energy needed to completely fracture the material. Materials showing good impact resistance, as well as ductile materials, are generally those with high moduli of toughness. The resilience & toughness integrals can be calculated from stress-strain data via methods such as [https://www.youtube.com/watch?v=R8g3B2iySA4&ab_channel=StephanieGlen trapezoidal Riemann sums in Excel].

During loading, the area under the stress-strain curve is the strain energy per unit volume absorbed by the material. Conversely, the area under the unloading curve is the energy released by the material. In the elastic range, these areas are equal and no net energy is absorbed. But if the material is loaded into the plastic range as shown above, the energy absorbed exceeds the energy released and the difference is dissipated as heat.

== Compression ==
Materials that exhibit high tensile strength tend to (but do not always!) exhibit low compressive strength. Likewise, materials high in compressive strength tend to exhibit low tensile strength. Therefore, compression testing is often used on brittle materials such as concrete, metals, plastics, ceramics, composites, and corrugated materials like cardboard. These materials are often used in a load-bearing capacity where their integrity under compressive forces is critical.

Unlike tensile tests, which are usually conducted to determine the tensile properties of a specific material, compression tests are often performed on finished products. Common items such as tennis balls, golf balls, water bottles, protective cases, plastic pipes, and furniture are all examples of products that need to be evaluated for their compressive strength. For example, an engineer may want to conserve plastic by creating water bottles with thinner walls, but the bottles must still be strong enough to be packed in pallets and stacked on top of each other for transport. Compression testing can help the engineer fine tune the balance between product strength and material conservation.

As long as the loads are sufficiently small (stresses less than the proportional limit), in many materials the relations outlined for tensile testing apply equally well in compression. The expression for deformation <math> (\delta) </math> from a given load

<math> \delta = \frac{FL}{AE} </math>,

applies just as in tension, with negative values for δ and F indicating compression. Further, the modulus E is the same in tension and compression to a good approximation, and the stress-strain curve simply extends as a straight line into the third quadrant as shown below.

There are some practical difficulties in performing stress-strain tests in compression. If excessively large loads are mistakenly applied in a tensile test, perhaps by wrong settings on the testing machine, the specimen simply breaks and the test must be repeated with a new specimen. But in compression, a mistake can easily damage the load cell or other sensitive components, since even after specimen failure the loads are not necessarily relieved. This is why when designing a method for the Instron tester, there must always be a second stop condition at 28kN load. The ultimate compressive strength of a material is the value of compressive stress reached when the material fails completely. When brittle materials reach their ultimate compressive strength they are crushed, and the load drops drastically. Materials with higher ductility, (most plastics) do not rupture, but instead continue deforming until the load is no longer being applied to the specimen, but rather between the two compression platens. In these cases, compressive strength can be reported as specific deformations such as 1%, 5%, or 10% of the test specimen's original height. <ref name="Instron"> Instron. (n.d.). What is Compression Testing? https://www.instron.us/en-us/our-company/library/test-types/compression-test. </ref>

== Bend Testing ==
[[File:BendVMDiagram.PNG|thumb|Diagram of a three point bend test, with graphs of bending moment ''M'', shear ''Q'' and deflection ''w'' <ref name="Penn"> Penn Center for Musculoskeletal Disorders. Three Point and Four Point Bending | Penn Center for Musculoskeletal Disorders | Perelman School of Medicine at the University of Pennsylvania. (n.d.). https://www.med.upenn.edu/pcmd/3pt-4pt-bending.html. </ref>]]
In bending tests, standardized, mostly cylindrical specimens are placed centrally on a test fixture. <ref name="GOM"> Bending test: Suitable for both brittle and ductile materials. (n.d.). https://www.gom.com/en/topics/bend-test. </ref> The rounded support rollers (bearings) are arranged parallel to each other at a certain distance (support width). The diameter of the cylindrical specimen is proportional to the support width of the bearings. The test punch, which moves down slowly and at a constant speed, loads the sample with increasing force until it breaks or reaches the previously determined deformation. Flexural modulus (elastic modulus in bending), stress-strain behavior, and failure limits can all be obtained using a bend test. <ref name="Bruker"> 3-Point Bend Testing. Bruker. (n.d.). https://www.bruker.com/en/products-and-solutions/test-and-measurement/tribometers-and-mechanical-testers/3-point-bend-testing.html. </ref> The 3-point bending test is the most frequently performed bending test. However, it has the disadvantage that in addition to the compressive and tensile forces exerted, transverse forces are also effective in the material.

During the test, the values of the bending force and deflection are recorded, which are then used to determine the material characteristics. The test sequence is plotted in a stress-strain curve and can also be recorded with a video camera. Bending tests are performed to obtain information about the bending behavior of the tested material from the single-axis bending stress. In case of brittle materials, the bending strength is determined this way. For ductile materials, the limit yield point, greatest possible bending angle, and Young’s modulus are determined.

Calculation of the flexural stress <math>\sigma_f</math>

:<math>\sigma_f = \frac{3 F L}{2 b d^2}</math> for a rectangular cross section

:<math>\sigma_f = \frac{F L}{\pi R^3}</math> for a circular cross section<ref name=Biomaterials>"Chapter 4 Mechanical Properties of Biomaterials". Biomaterials – The intersection of Biology and Material Science. New Jersey, United States: Pearson Prentice Hall. 2008. p. 152.</ref>

Calculation of the flexural strain <math>\epsilon_f</math>

:<math>\epsilon_f = \frac{6Dd}{L^2}</math>

Calculation of flexural modulus <math>E_f</math><ref name="Zweben"> Zweben, C., W. S. Smith, and M. W. Wardle (1979), "Test methods for fiber tensile strength, composite flexural modulus, and properties of fabric-reinforced laminates", Composite Materials: Testing and Design (Fifth Conference), ASTM International</ref>

:<math>E_f = \frac{L^3 m}{4 b d^3}</math>

in these formulas the following parameters are used:
* <math>\sigma_f</math> = Stress in outer fibers at midpoint, (MPa)
* <math>\epsilon_f</math> = Strain in the outer surface, (mm/mm)
* <math>E_f</math> = flexural Modulus of elasticity,(MPa)
* <math>F</math> = load at a given point on the load deflection curve, (N)
* <math>L</math> = Support span, (mm)
* <math>b</math> = Width of test beam, (mm)
* <math>d</math> = Depth or thickness of tested beam, (mm)
* <math>D</math> = maximum deflection of the center of the beam, (mm)
* <math>m</math> = The gradient (i.e., slope) of the initial straight-line portion of the load deflection curve, (N/mm)

* <math>R</math> = The radius of the beam, (mm)

In a bending test, the bending stress is greatest in the center of the specimen (highest deflection). At this point, the greatest bending moment is always present. From the central pressure point, the bending moment decreases linearly in both directions toward the bearings. The material is subjected to pressure on its inner side and tension on its outer side. In the outer fibers of the specimen, the bending stress (tensile and compressive stress) is greatest and decreases inwards toward the neutral fiber.

If a partially plastically deformed specimen is relieved during the bending test by raising the test punch, only the internal stresses (residual stresses) present in the material and the resulting torque are still effective. This will partially reshape the sample.

== Bending Behavior of Ductile Materials ==
If the bending stress in the sample made of a ductile material is lower than the limit stress of the plastic deformation, the bending stress is exclusively elastic. As the bending stress increases, the yield strength is exceeded first in the peripheral areas of the specimen. These areas then deform plastically (the so-called material flow). The limit yield point is the limit bending stress up to which easily deformable materials can be loaded by bending without permanent deformation in the marginal area.

The moment this kind of deformation occurs can be determined directly from the deflection-force diagram, in a similar manner to how the yield strength is found in a tensile test. With deflection increasing steadily, more and more internal areas of the specimen are involved in the plastic deformation. This is a result of the stress increase. For steels, for example, the limit yield point is between 10 to 20 percent higher than the yield strength due to the linear stress increase. If the yield strength is exceeded in the edge fibers during the bending test, the inner and exclusively elastically stressed fibers impede the flow movement. Bending tests with ductile materials are different from those performed with brittle materials: Tough materials can be subjected to extreme plastic deformation, but they cannot be broken, no matter how strong the applied force is. Therefore, a bending test with a ductile sample is finished when the yield point is exceeded. The bending strength of ductile materials is determined by the point in time at which the plastic deformation occurs.

== Bending Behavior of Brittle Materials: ==
Specimens made of brittle materials show a different bending behavior during materials testing. They break without clearly visible material flow behavior. Therefore, the determination of the limit yield point is more complicated for brittle materials. In order to be able to determine the bending strength nevertheless, the maximum bending stress at which the sample breaks is determined. However, the bending strength is a fictitious value that is not identical to the bending stress actually occurring in the material. Another characteristic of bending tests with brittle materials is the fracture deflection. This technical term describes the greatest possible deflection of a specimen shortly before fracture.

The fracture deflection depends on the support width: Larger distances between the bearings allow for greater deflections. In order to check the strength of brittle materials, the bending test is often more suitable than the tensile test, because the materials are subjected to bending stress only. If this sample were to be subjected to a tensile test, it would break prematurely and measurement problems would occur. For certain brittle materials, the tensile test is therefore replaced by the bending test. These materials include thermosetting sheets and molding materials, thermoplastic injection molding compounds, and fiber-reinforced plastics.

== Related Theory ==
* [[Cyclic Loading]]
* [[Stress Theory]]

== References ==
<references />

[[Category:Equipment|meas]]

Category:Software

2021-06-09T14:42:11Z

Akulaksizoglu3: /* General */

List of distributable software from the MILL and software available to all GT students.

== General ==
* [[MATLAB]]
* COMSOL
*OriginPro

== Characterization ==
* PhenomImageViewer ([[Scanning Electron Microscope (SEM)|SEM]])
* CrystalMaker ([[X-ray Diffractometer (XRD)|XRD]])
* MDI JADE Pro ([[X-ray Diffractometer (XRD)|XRD]])

== Measurement ==
* n/a

== Processing ==
* Ultimaker Cura
* Prusa Slicer

Category:Software

2021-06-09T14:41:33Z

Akulaksizoglu3: /* General */

List of distributable software from the MILL and software available to all GT students.

== General ==
* MATLAB
* COMSOL
*OriginPro

== Characterization ==
* PhenomImageViewer ([[Scanning Electron Microscope (SEM)|SEM]])
* CrystalMaker ([[X-ray Diffractometer (XRD)|XRD]])
* MDI JADE Pro ([[X-ray Diffractometer (XRD)|XRD]])

== Measurement ==
* n/a

== Processing ==
* Ultimaker Cura
* Prusa Slicer

Microhardness

2021-06-09T14:40:18Z

Akulaksizoglu3: final form

{|class="infobox"
!style="font-size:135%;text-align:center;" | LECO Microhardness Tester
|-
|[[File:Microhardness-052621.png|center|300px]]
|-
|'''Objectives''': 10x, 50x
|-
|'''Indenters''': Vickers, Knoop
|-
|'''Load Force''': 5-2000gf (0.05-19.61N)
|-
|'''Dwell Time''': 0-20s
|-
|'''Standard Comformation:''' ASTM E-384, JIS B-7734, ISO 4545 (Knoop), and ISO 6507 (Vickers)
|}

The LECO LM 248 AT is a hardness tester that is designed to measure the hardness of materials on the microscopic level. The machine can magnify a surface as much as 50x and measure the hardness of a sample on the Vickers, Knoop, and Rockwell C scales. Hardness testing is used for two general characterizations: material characteristics (such as confirming material, testing hardenability, and predicting tensile strength) or functionality (testing wear resistance, toughness, and resistance to impact).

== Introduction ==

Hardness tests are a simple method to determine the resistance of a metal to plastic deformation.<ref name="Meyers">Meyers, M., & Chawla, K. (2016). Hardness. In Mechanical Behavior of Materials (2nd ed., pp. 214–225). chapter, Cambridge University Press.</ref> Indentation tests constitute the vast majority of hardness tests and can be divided into three classes: nanoindentation, microindentation, and macroindentation (based on the indentation load used). The smaller the indentation, the harder the material. Both the yield stress and the work-hardening characteristics of the metal are important in determining the hardness. Hardness is not considered a fundamental property of a material; it represents a quantity measure on an arbitrary scale. There are several different methods used for hardness testing, which use varying shapes of indenters and loads. The MILL’s Leco LM 248AT comes with Vickers and Knoop indenters and calculates Rockwell C hardness from whichever of these scales is being used.

== Preparation ==

The following precautions are recommended for reproducible results in hardness testing:<ref name="NEWAGE"> NEWAGE Hardness Testers. (n.d.). Hardness Testing Basics. NEWAGE Hardness Testers - Rockwell Testers, Brinell Testers, Microhardness Testers, Optical Systems and Hardness Testing Software. https://www.hardnesstesters.com/test-types/hardness-testing-basics. </ref>

# The indenter and anvil should be clean and well seated.
# The surface to be tested should be clean, dry, smooth, and free from oxide. A rough-ground surface is usually adequate for a Vickers macro-hardness test, while the Knoop indenter requires pre-polishing of the surface to a microscopic grade.
# The surface should be flat and perpendicular to the indenter. Any specimen movement during indentation can cause deformed indents.
# The thickness of the specimen should be such that a mark or bulge is not produced on the reverse side of the piece. It is recommended that the thickness be at least 10 times the depth of the indentation. Tests should be made on only a single thickness of material.
# The spacing between indentations should be at least 3 times the longest dimension of the indentation, to avoid interaction between the work-hardening regions.

== Macro-indentation Tests ==

[[File:Hardness1.png|thumb|600px|Diagram of Rockwell Test]]

The Rockwell test is popular and convenient, since there is no need to measure the depth or width of the indentation optically. This testing procedure is illustrated below. A preload is applied prior to the application of the main load. The dial of the machine provides a number that is related to the depth of the indentation produced by the main load. A Brale indenter, a diamond cone with an angle of 120°, is used in Rockwell C tests. The Rockwell C scale is usually used for harder steels.

The Vickers test uses a diamond pyramidal indenter with a square base, with an angle between the faces of 136°. One of the known advantages of the Vickers test is that one indenter covers all the materials, from the softest to the hardest. The load is increased with hardness, and there is a continuity in scale. The Vickers hardness (HV) is computed from the equation below:

<math>HV = \frac{2P \cdot \mathrm{sin(\alpha/2)}}{d^2} \approx \frac{1.8544P}{d^2}</math>

where P is the applied load (in kgf), d is the average length of the diagonals (in mm), and α is the angle between the opposite faces of the indenter (136°). Conversion to MPa is accomplished by multiplying this value by 9.81. After the indentation, both diagonals of impression are measured, and their average is taken. If the surface is cylindrical or spherical, a correction factor (ASTM Standard E92, Tables 4 through 6) has to be introduced. Microhardness tests utilize a load lighter than 200 gf, and very minute impressions are thus formed; a load of 200 gf produces an indentation of about 50 μm for a medium-hardness metal. These tests are ideally suited to investigate changes in hardness at the microscopic scale. One can measure the hardness of a second-phase particle and identify regions within a grain where differences in hardness occur. Micro-hardness tests are also used to perform routine tests on very small precision components, such as parts of watches. When a metal is alloyed, the distribution of the solute is not even throughout the grain, due to the stress fields produced by the solute atom. The solute atoms often tend to segregate at the grain boundaries, significantly increasing or decreasing the hardness in these areas. This effect can be noted at extremely low concentrations of solute (a few parts per million).

== Micro-indentation Tests ==
[[File:Screen Shot 2021-06-09 at 10.18.04 AM.png|thumb|539x539px|Shapes of Vickers (VK) and Knoop (HK) indenters, depth and minimum sample thickness requirements of each indenter.<ref name=":0">LECO Corporation. (2017). ''Lm Series Digital Microindentation Tester Instruction Manual''.</ref>]]
The two most common micro-indentation tests are the Knoop and Vickers tests. The Knoop indenter is an elongated square pyramid, while Vickers indenter is a regular square pyramid.

The hardness is obtained from the surface area of the impression and is given by:

<math> KHN = \frac {14229P}{L^2} </math>

where P is the load of gf and L is the length of the major diagonal, in micrometers.

====== Dwell Time ======
The ASTM specification for dwell time is 10 to 15 seconds. The dwell time can be changed to meet a specific requirement. As a general rule, a shorter load time is preferable as it reduces the chances of outside influence (vibration, etc.) on the tester.<ref name=":0" />

====== Distance Between Indentations ======
Spacing indentations too close together can cause the test piece to become “work hardened” in that area, resulting in false readings. Be sure to maintain proper spacing between indents, in all directions.

====== Vickers vs. Knoop ======
The Vickers Hardness test has two significant advantages:

* Geometrically similar indentations and relatively constant hardness values are obtained, regardless of the loads applied, as long as test specimens are homogeneous.
* Materials ranging from extremely soft to extremely hard can be tested without changing loads.

The Knoop Hardness test should only be used for measurement of extremely thin plates and brittle materials that cannot be measured by ordinary Vickers Hardness tests. The geometric shape of Knoop indents does vary with the load used.

====== Micro-hardness vs. Macro-hardness ======
There are several problems with the extrapolation of micro-indentation testing to macro indentation results. First, almost invariably, the micro-hardness of any material is higher than its standard macro-hardness. Additionally, the micro-hardness varies with load. Second, there is a tendency for the micro-hardness to increase (up to a few grams); then the hardness value drops with load. At very low loads, one is essentially measuring the hardness of a single grain; the indenter ‘‘sees” a single crystal, and the plastic deformation produced by the indentation is contained in this grain. As the load is increased, plastic deformation of adjoining grains is involved, and a truly polycrystalline deformation regimen is achieved. Grain size has a marked effect on the yield strength and work-hardening characteristics of metals. Yet another potential source of error is the work-hardening introduced in the surface by polishing. The effect of crystallographic orientation, when the impression is restricted to a single grain, is of utmost importance. It is well known that both the yield stress and the work-hardening are dependent on the crystallographic orientation of the material.

== Relationships Between Yield Stress and Hardness ==

For non-work-hardening (brittle) materials, hardness is equal to three times the yield stress (H = 3σ<sub>y</sub>). Since there is a lot of plastic deformation under the indenter, in work-hardening (ductile) materials yield strain cannot be used. The mean plastic strain under the indenter is described by the following equation:

<math> {ε_p} = \frac{d′}{5D} </math>

where d′ is the diameter at the top of the pileup and D is the diameter of the indenter. For d′/D = 0.375, a reasonable value for indentation, the plastic strain, εp = 0.075. Hence, for work-hardening metals, one should take the flow stress at a plastic strain of 0.375 before multiplying it by 3 for a good correlation with the hardness.
== Converting Between Scales ==
If the desired hardness scale cannot be measured by the Leco tester, a conversion table such as [https://pgisteel.com/hardness-conversion-chart/ this]<ref name="Conversion"> ''Hardness Conversion Chart''. PGI Steel. (n.d.). https://pgisteel.com/hardness-conversion-chart/ </ref>. may be used to find the value on the desired scale. It should be noted that not all hardness scales cover the same range or are designed for the same materials.

== References ==
<references />

[[Category:Equipment|meas]]

File:Screen Shot 2021-06-09 at 10.18.04 AM.png

2021-06-09T14:22:49Z

Akulaksizoglu3:

Shapes of Vickers (VK) and Knoop (HK) indenters, depth and minimum sample thickness requirements of each indenter.

Microhardness

2021-06-09T14:04:24Z

Akulaksizoglu3: /* Microindentation Tests */

{|class="infobox"
!style="font-size:135%;text-align:center;" | LECO Microhardness Tester
|-
|[[File:Microhardness-052621.png|center|300px]]
|-
|'''Objectives''': 10x, 50x
|-
|'''Indenters''': Vickers, Knoop
|-
|'''Load Force''': 5-2000gf (0.05-19.61N)
|-
|'''Dwell Time''': 0-20s
|}

The LECO LM 248 AT is a hardness tester that is designed to measure the hardness of materials on the microscopic level. The machine can magnify a surface as much as 50x and measure the hardness of a sample on the Vickers, Knoop, and Rockwell C scales. Hardness testing is used for two general characterizations: material characteristics (such as confirming material, testing hardenability, and predicting tensile strength) or functionality (testing wear resistance, toughness, and resistance to impact).

== Introduction ==

Hardness tests are a simple method to determine the resistance of a metal to plastic deformation.<ref name="Meyers">Meyers, M., & Chawla, K. (2016). Hardness. In Mechanical Behavior of Materials (2nd ed., pp. 214–225). chapter, Cambridge University Press.</ref> Indentation tests constitute the vast majority of hardness tests and can be divided into three classes: nanoindentation, microindentation, and macroindentation (based on the indentation load used). The smaller the indentation, the harder the material. Both the yield stress and the work-hardening characteristics of the metal are important in determining the hardness. Hardness is not considered a fundamental property of a material; it represents a quantity measure on an arbitrary scale. There are several different methods used for hardness testing, which use varying shapes of indenters and loads. The MILL’s Leco LM 248AT comes with Vickers and Knoop indenters and calculates Rockwell C hardness from whichever of these scales is being used.

== Preparation ==

The following precautions are recommended for reproducible results in hardness testing:<ref name="NEWAGE"> NEWAGE Hardness Testers. (n.d.). Hardness Testing Basics. NEWAGE Hardness Testers - Rockwell Testers, Brinell Testers, Microhardness Testers, Optical Systems and Hardness Testing Software. https://www.hardnesstesters.com/test-types/hardness-testing-basics. </ref>

# The indenter and anvil should be clean and well seated.
# The surface to be tested should be clean, dry, smooth, and free from oxide. A rough-ground surface is usually adequate for a Vickers macrohardness test, while the Knoop indenter requires prepolishing of the surface to a microscopic grade.
# The surface should be flat and perpendicular to the indenter.
# The thickness of the specimen should be such that a mark or bulge is not produced on the reverse side of the piece. It is recommended that the thickness be at least 10 times the depth of the indentation. Tests should be made on only a single thickness of material.
# The spacing between indentations should be at least 3 times the longest dimension of the indentation, to avoid interaction between the work-hardening regions.

== Macroindentation Tests ==

[[File:Hardness1.png|thumb|600px|Diagram of Rockwell Test]]

The Rockwell test is popular and convenient, since there is no need to measure the depth or width of the indentation optically. This testing procedure is illustrated below. A preload is applied prior to the application of the main load. The dial of the machine provides a number that is related to the depth of the indentation produced by the main load. A Brale indenter, a diamond cone with an angle of 120°, is used in Rockwell C tests. The Rockwell C scale is usually used for harder steels.

The Vickers test uses a diamond pyramidal indenter with a square base, with an angle between the faces of 136°. One of the known advantages of the Vickers test is that one indenter covers all the materials, from the softest to the hardest. The load is increased with hardness, and there is a continuity in scale. The Vickers hardness (HV) is computed from the equation below:

<math>HV = \frac{2P \cdot \mathrm{sin(\alpha/2)}}{d^2} \approx \frac{1.8544P}{d^2}</math>

where P is the applied load (in kgf), d is the average length of the diagonals (in mm), and α is the angle between the opposite faces of the indenter (136°). Conversion to MPa is accomplished by multiplying this value by 9.81. After the indentation, both diagonals of impression are measured, and their average is taken. If the surface is cylindrical or spherical, a correction factor (ASTM Standard E92, Tables 4 through 6) has to be introduced. Microhardness tests utilize a load lighter than 200 gf, and very minute impressions are thus formed; a load of 200 gf produces an indentation of about 50 μm for a medium-hardness metal. These tests are ideally suited to investigate changes in hardness at the microscopic scale. One can measure the hardness of a second-phase particle and identify regions within a grain where differences in hardness occur. Micro-hardness tests are also used to perform routine tests on very small precision components, such as parts of watches. When a metal is alloyed, the distribution of the solute is not even throughout the grain, due to the stress fields produced by the solute atom. The solute atoms often tend to segregate at the grain boundaries, significantly increasing or decreasing the hardness in these areas. This effect can be noted at extremely low concentrations of solute (a few parts per million).

== Microindentation Tests ==

[[File:Knoop.PNG|thumb|Diagram of Knoop Indenter]]

The two most common microindentation tests are the Knoop and Vickers tests. The Knoop indenter is an elongated pyramid.

The hardness is obtained from the surface area of the impression and is given by:

<math> KHN = \frac {14.229P}{L^2} </math>

where P is the load of kgf and L is the length of the major diagonal, in mm.

====== Vickers vs. Knoop ======
The very shallow Knoop impression is helpful in testing thin components, such as electro-deposits or hardened layers, or brittle materials.

There are several problems with the extrapolation of micro-indentation testing to macro indentation results. First, almost invariably, the micro-hardness of any material is higher than its standard macro-hardness. Additionally, the micro-hardness varies with load. Second, there is a tendency for the micro-hardness to increase (up to a few grams); then the hardness value drops with load. At very low loads, one is essentially measuring the hardness of a single grain; the indenter ‘‘sees” a single crystal, and the plastic deformation produced by the indentation is contained in this grain. As the load is increased, plastic deformation of adjoining grains is involved, and a truly polycrystalline deformation regimen is achieved. Grain size has a marked effect on the yield strength and work-hardening characteristics of metals. Yet another potential source of error is the work-hardening introduced in the surface by polishing. The effect of crystallographic orientation, when the impression is restricted to a single grain, is of utmost importance. It is well known that both the yield stress and the work-hardening are dependent on the crystallographic orientation of the material.

== Relationships Between Yield Stress and Hardness ==

For non-work-hardening (brittle) materials, hardness is equal to three times the yield stress (H = 3σ<sub>y</sub>). Since there is a lot of plastic deformation under the indenter, in work-hardening (ductile) materials yield strain cannot be used. The mean plastic strain under the indenter is described by the following equation:

<math> {ε_p} = \frac{d′}{5D} </math>

where d′ is the diameter at the top of the pileup and D is the diameter of the indenter. For d′/D = 0.375, a reasonable value for indentation, the plastic strain, εp = 0.075. Hence, for work-hardening metals, one should take the flow stress at a plastic strain of 0.375 before multiplying it by 3 for a good correlation with the hardness.
== Converting Between Scales ==
If the desired hardness scale cannot be measured by the Leco tester, a conversion table such as [https://pgisteel.com/hardness-conversion-chart/ this]<ref name="Conversion"> ''Hardness Conversion Chart''. PGI Steel. (n.d.). https://pgisteel.com/hardness-conversion-chart/ </ref>. may be used to find the value on the desired scale. It should be noted that not all hardness scales cover the same range or are designed for the same materials.

== References ==
<references />

[[Category:Equipment|meas]]