Mechanical Testing - Revision history

ObordenMEASURE: Added/adjusted some citations

2025-06-26T19:31:17Z

Added/adjusted some citations

ObordenMEASURE: Added paragraph about dog bone samples, and link to STL file

2025-06-26T19:25:43Z

Added paragraph about dog bone samples, and link to STL file

← Older revision		Revision as of 15:25, 26 June 2025
Line 65:		Line 65:

	== Tensile Testing & Engineering Stress-Strain Curves ==		== Tensile Testing & Engineering Stress-Strain Curves ==
	[[File:Tensile Test Instron.jpeg\|thumb\|~~207x207px~~\|Tensile Test Set Up on Instron tester<ref>Borden, O. 11 June 2025</ref>]]		[[File:Tensile Test Instron.jpeg\|thumb\|125x125px\|Tensile Test Set Up on Instron tester<ref>Borden, O. 11 June 2025</ref>]]
	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-displacement 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.		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-displacement 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:ASTM Dogbone Standard.png\|center\|thumb\|274x274px\|ASTM dimensions for 3D printed dog bone standard]]
			The ASTM standard for tensile testing is a dog bone shape. This ensures that the break happens near the center of the sample, and not near the grips. This avoids corrupting the data due to force applied by the grips on the material. By clicking [https://drive.google.com/file/d/1GLtQdBHNnlCw7U8GfFs6V392wYZenM0L/view?usp=sharing here] you can access a .stl file for the ASTM dog bone standard.

	A stress-strain curve always has the same 3 sections: elastic deformation, plastic deformation, and fracture. These three section occur differently in different materials and have subcategories as described below.		A stress-strain curve always has the same 3 sections: elastic deformation, plastic deformation, and fracture. These three section occur differently in different materials and have subcategories as described below.

ObordenMEASURE: Added details on second Mark-10 (FS05) to overview, and updated the Instron bio to show it now has 4-point-bend capabilities.

2025-06-17T14:53:15Z

Added details on second Mark-10 (FS05) to overview, and updated the Instron bio to show it now has 4-point-bend capabilities.

← Older revision		Revision as of 10:53, 17 June 2025
Line 2:		Line 2:
	!		!
	!style="font-size:135%;text-align:center;" \| Mark-10 ESM303 [https://sites.gatech.edu/mse-mill/sop/mark-10/ [SOP<nowiki>]</nowiki>]		!style="font-size:135%;text-align:center;" \| Mark-10 ESM303 [https://sites.gatech.edu/mse-mill/sop/mark-10/ [SOP<nowiki>]</nowiki>]
	!style="font-size:135%;text-align:center;" \| Instron 5967 [https://sites.gatech.edu/mse-mill/sop/instron/ [SOP<nowiki>]</nowiki>]		!<big>'''Mark-10 FS05 [https://mill.mse.gatech.edu/sop/mark-10-fs05/ <nowiki>[SOP]</nowiki>]'''</big>
			! style="font-size:135%;text-align:center;" \| Instron 5967 [https://sites.gatech.edu/mse-mill/sop/instron/ [SOP<nowiki>]</nowiki>]
	\|-		\|-
	\|                          \|\|[[File:Mark10-052621.png\|center\|250px]]\|\|[[File:Instron-052621.png\|center\|250px]]		\|                          \|\|[[File:Mark10-052621.png\|center\|250px]]
			\|[[File:Unknown.jpg\|frameless\|359x359px]]
			\|[[File:Instron-052621.png\|center\|250px]]
	\|-		\|-
	\|'''Load Cells''':\|\|500 mN, 25 N, 500 N, 1500 N\|\|30 kN		\|'''Load Cells''':\|\|500 mN, 25 N, 500 N, 1500 N
			\|0.5 N, 25 N, 250 N, 2.5 kN\|\|30 kN
	\|-		\|-
	\|'''Load Capacity''':\|\|1.5 kN @ up to 610 mm/min\|\|30 kN		\|'''Load Capacity''':\|\|1.5 kN @ up to 610 mm/min
			\|2.2 kN\|\|30 kN
	\|-		\|-
	\|'''Speed range''':\|\|13 - 330 mm/min\|\|0.001 mm/min - 1000 mm/min		\|'''Speed range''':\|\|13 - 330 mm/min
			\|0.5 - 1,100 mm/min\|\|0.001 mm/min - 1000 mm/min
	\|-		\|-
	\|'''Travel range''':\|\|45.7 cm\|\|1.212 m		\|'''Travel range''':\|\|45.7 cm
			\|457 mm\|\|1.212 m
	\|-		\|-
	\|'''Max width''':\|\|n/a\|\|0.418 m		\|'''Max width''':\|\|n/a
			\|n/a\|\|0.418 m
	\|}		\|}

	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 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.		The Mark-10 FS05 Mechanical Tester is a mechanical testing frame with attachments for tensile, 3 and 4 point bend, compressive, and peel tests. It can also preform cyclic test procedures. It has 0.5 N, 25 N, 250 N, and 2.5 kN load cells.

			The Instron Mechanical Tester is a mechanical testing frame capable of testing materials under tensile, compressive, and 3 or 4-point-bending modes. This machine is equipped with a 30kN load cell.

	== Loading ==		== Loading ==

ObordenMEASURE: /* Compression */ Added images of compression and bend test set ups.

2025-06-17T13:51:11Z

Compression: Added images of compression and bend test set ups.

← Older revision		Revision as of 09:51, 17 June 2025
Line 55:		Line 55:

	== Tensile Testing & Engineering Stress-Strain Curves ==		== Tensile Testing & Engineering Stress-Strain Curves ==
	[[File:Tensile Test Instron.jpeg\|thumb\|207x207px\|Tensile Test Set Up on Instron tester<ref>Borden, O. June 2025</ref>]]		[[File:Tensile Test Instron.jpeg\|thumb\|207x207px\|Tensile Test Set Up on Instron tester<ref>Borden, O. 11 June 2025</ref>]]
	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-displacement 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.		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-displacement 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.

Line 123:		Line 123:

	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.		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.
			[[File:Instroncompression.jpg\|thumb\|285x285px\|Compression Test on Instron Instrument<ref>Borden, O. 11 June 2025</ref>]]
	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		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

Line 149:		Line 149:

	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>		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>
			[[File:Mark10 3point.jpg\|thumb\|3 Point Bend Test set up on Mark 10 Machine<ref>Borden, O. 11 June 2025</ref>]]
	:<math>E_f = \frac{L^3 m}{4 b d^3}</math>		:<math>E_f = \frac{L^3 m}{4 b d^3}</math>

Line 187:		Line 187:
	<references />		<references />

	[[~~index~~.php?title=Category:Equipment\|meas]]		[[Index.php?title=Category:Equipment\|meas]]

ObordenMEASURE: /* Tensile Testing & Engineering Stress-Strain Curves */ Added image of Tensile Test

2025-06-17T13:44:48Z

Tensile Testing & Engineering Stress-Strain Curves: Added image of Tensile Test

← Older revision		Revision as of 09:44, 17 June 2025
Line 42:		Line 42:

	=== Engineering Stress/Strain ===		=== Engineering Stress/Strain ===
	In many applications, a simpler form of strain, commonly called engineering or nominal strain, is used. This type of strain 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>]]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>		<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.

			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:

			<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.		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 ==		== Tensile Testing & Engineering Stress-Strain Curves ==
			[[File:Tensile Test Instron.jpeg\|thumb\|207x207px\|Tensile Test Set Up on Instron tester<ref>Borden, O. June 2025</ref>]]
	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-displacement 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.		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-displacement 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.

Line 182:		Line 187:
	<references />		<references />

	[[Category:Equipment\|meas]]		[[index.php?title=Category:Equipment\|meas]]

Mjimenez47 at 19:57, 14 June 2025

2025-06-14T19:57:21Z

← Older revision		Revision as of 15:57, 14 June 2025
Line 97:		Line 97:
	Ductile metals often have true stress-strain relations that can be described by a simple power-law relation of the form:		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>		<math> \sigma_t = A\epsilon_tn \rightarrow 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.		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.

Mjimenez47 at 19:04, 14 June 2025

2025-06-14T19:04:00Z

← Older revision		Revision as of 15:04, 14 June 2025
Line 90:		Line 90:
	== True Stress-Strain Curve ==		== 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> ]]		[[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:		During elastic deformation, the change in cross-sectional area is less than 1% for most metals and ceramics; thus <math> \sigma_e \approx \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> \epsilon_t =ln(1+\epsilon_e) </math>

Dnanji: Dnanji moved page Mechanical Tester to Mechanical Testing

2022-11-09T16:57:15Z

Dnanji moved page Mechanical Tester to Mechanical Testing

← Older revision		Revision as of 12:57, 9 November 2022
(No difference)

Tbowman36: /* Stress and Strain */

2022-09-15T20:43:35Z

Stress and Strain

← Older revision		Revision as of 16:43, 15 September 2022
Line 22:		Line 22:

	== Loading ==		== Loading ==
	[[File:Loading.PNG\|thumb\|~~225x225px~~\|left\|1. Compression 2. Tension 3. Shear 4. Torsion 5. Bending]]		[[File:Loading.PNG\|thumb\|199x199px\|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>		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>

Tbowman36: formatting edits for clarity (in stress and strain sections). made load picture smaller

2022-09-15T20:42:49Z

formatting edits for clarity (in stress and strain sections). made load picture smaller

← Older revision		Revision as of 16:42, 15 September 2022
Line 22:		Line 22:

	== Loading ==		== Loading ==
	[[File:Loading.PNG\|thumb\|~~350px~~\|left\|1. Compression 2. Tension 3. Shear 4. Torsion 5. Bending]]		[[File:Loading.PNG\|thumb\|225x225px\|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>		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>
Line 31:		Line 31:

	== Stress and Strain ==		== Stress and Strain ==

			=== True Stress/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:		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>		<math> \sigma_t =\frac{F}{A}, </math> Where ''F'' is force, ''A'' is area, and <math> \sigma </math> is stress.

	~~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:		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>		<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.

	~~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		=== Engineering Stress/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>		<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>		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.

	~~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.		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 ==		== Tensile Testing & Engineering Stress-Strain Curves ==

← Older revision		Revision as of 15:31, 26 June 2025
Line 67:		Line 67:
	[[File:Tensile Test Instron.jpeg\|thumb\|125x125px\|Tensile Test Set Up on Instron tester<ref>Borden, O. 11 June 2025</ref>]]		[[File:Tensile Test Instron.jpeg\|thumb\|125x125px\|Tensile Test Set Up on Instron tester<ref>Borden, O. 11 June 2025</ref>]]
	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-displacement 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.		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-displacement 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:ASTM Dogbone Standard.png\|center\|thumb\|274x274px\|ASTM dimensions for 3D printed dog bone standard]]		[[File:ASTM Dogbone Standard.png\|center\|thumb\|274x274px\|ASTM dimensions for 3D printed dog bone standard<ref name=":0">Lmpeeke. (Oct 1, 2018) ASTM D638 Type IV Dog bone Tensile sample. https://www.thingiverse.com/thing:3131427</ref>]]
	The ASTM standard for tensile testing is a dog bone shape. This ensures that the break happens near the center of the sample, and not near the grips. This avoids corrupting the data due to force applied by the grips on the material. By clicking [https://drive.google.com/file/d/1GLtQdBHNnlCw7U8GfFs6V392wYZenM0L/view?usp=sharing here] you can access a .stl file for the ASTM dog bone standard.		The ASTM standard for tensile testing is a dog bone shape. This ensures that the break happens near the center of the sample, and not near the grips. This avoids corrupting the data due to force applied by the grips on the material. By clicking [https://drive.google.com/file/d/1GLtQdBHNnlCw7U8GfFs6V392wYZenM0L/view?usp=sharing here]<ref name=":0" /> you can access a .stl file for the ASTM dog bone standard.

	A stress-strain curve always has the same 3 sections: elastic deformation, plastic deformation, and fracture. These three section occur differently in different materials and have subcategories as described below.		A stress-strain curve always has the same 3 sections: elastic deformation, plastic deformation, and fracture. These three section occur differently in different materials and have subcategories as described below.
Line 135:		Line 135:

	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.		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.
	[[File:Instroncompression.jpg\|thumb\|285x285px\|Compression Test on Instron Instrument<ref>Borden, O. 11 June 2025</ref>]]		[[File:Instroncompression.jpg\|thumb\|285x285px\|Compression Test on Instron Instrument<ref>Borden, O. (11 June 2025)</ref>]]
	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		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

Line 161:		Line 161:

	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>		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>
	[[File:Mark10 3point.jpg\|thumb\|3 Point Bend Test set up on Mark 10 Machine<ref>Borden, O. 11 June 2025</ref>]]		[[File:Mark10 3point.jpg\|thumb\|3 Point Bend Test set up on Mark 10 Machine<ref>Borden, O. (11 June 2025)</ref>]]
	:<math>E_f = \frac{L^3 m}{4 b d^3}</math>		:<math>E_f = \frac{L^3 m}{4 b d^3}</math>