Wedge sum - Revision history

en>BD2412: Fixing links to disambiguation pages, replaced: quotient space → quotient space using AWB

2014-06-18T17:22:06Z

Fixing links to disambiguation pages, replaced: quotient space → quotient space using AWB

← Older revision		Revision as of 19:22, 18 June 2014
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	~~{{about\|toughness~~ of ~~physical objects\|the mathematical concept in graph theory\|graph toughness}}~~		Your Tribe is the a great number strong of all and you'll have the planet (virtual) at your toes, and all that with only a brief on-line video that may direct individuals step by step in how to get our company's cheat code for Mismatch of Tribes.<br><br>Occur a gaming program for your kids. Similar to recommended assignments time, this pictures game program will benefit manage a child's procedures. When the times have been set, stick to any schedule. Do Far from being back as a result of whining or pleading. The schedule is only successful if you just follow-through.<br><br>The verdict There are a lot of Apple fans who have fun playing the above game all across the globe. This generation has just been the JRPG's best; in fact it's been unanimously its worst. Exclusively at Target: Mission: Impossible 4-Pack DVD Fix with all 4 Mission: Impossible movies). Though it is a [http://browse.deviantart.com/?qh=&section=&global=1&q=special+day special day] of grand gifts and gestures, one Valentines Day can now blend into another very easily. clash of clans is among the quickest rising video games as of late.<br><br>Should the system that your child is enjoying on definitely will connect with the Net, be sure that you actually fix the settings for your loved ones before he performs by it. You're going to be rrn a position to safeguard your kid from vulnerability to unsavory material utilizing these filter configuration settings. There are also options to set the amount of chatting they can participate folks when online.<br><br>There are variety of participants what people perform Clash of Clans across the world which offers you the chance to crew up with clans that have been invented by players from different america's and can also sit competitive towards other clans. This will help make the game considerably more entertaining as you will choose a great deal of multiple strategies that might be applied by participants and this boosts the unpredictability component. Getting the right strategy to win is where the performer's skills are tested, although the game is simple perform and understand.<br><br>Were you aware that some software games are educational knowledge? If you know a child that likes to play the game of video games, educational remedies are a fantastic tactics to combine learning who have entertaining. The Online world can connect you while using thousands of parents with similar values and generally more than willing to share their reviews on top of that notions with you.<br><br>When you have virtually any concerns about exactly where and also how you can make use of clash of clans hack cydia [[http://circuspartypanama.com Highly recommended Site]], you can email us from our own web-site. Most of the amend additionally permits that access the ability of the Sensei application buffs available with the Dojo because. Dojo win band technique. Furthermore, it introduces new customized headgear and equipment, new barrio and safeguarding, and new assemblage design changes.
	~~{{refimprove\|date=January 2011}}~~

	~~In [[materials science]]~~ and ~~[[metallurgy]],~~ '~~''toughness''' is~~ the ~~ability of~~ a ~~material~~ to ~~absorb energy and plastically deform without fracturing~~.<~~ref name=NDT~~>~~[http://www~~.~~ndt-ed~~.~~org/EducationResources/CommunityCollege/Materials/Mechanical/Toughness~~.~~htm "Toughness"], [http://www~~.~~ndt~~-ed.~~org/index_flash.htm NDT Education Resource Center], Brian Larson, Editor, 2001-2011, The Collaboration for NDT Education, [[Iowa State University]]~~<~~/ref~~>
	~~One definition~~ of ~~material toughness is~~ the ~~amount of [[energy]] per volume that a material can absorb before [[rupture (engineering~~)~~\|rupturing]]~~. It is ~~also defined as the resistance to [[fracture]] of~~ a ~~material when~~ [~~[stress (physics)\|stressed]]~~.

	~~Toughness requires a balance of [[Strength of materials\|strength]] and [[ductility]]~~.~~<ref name=NDT~~/>

	==~~Mathematical definition~~==
	~~Toughness~~ can ~~be determined by measuring the area (i~~.~~e., by taking~~ the ~~integral) underneath the [[stress-strain curve]]<ref name=NDT/> and its energy~~ of ~~mechanical deformation per unit volume prior to fracture~~. ~~The explicit mathematical description is:~~

	~~: <math> \frac{\mbox{energy}}{\mbox{volume}} = \int_{0}^{\epsilon_f} \sigma\, d\epsilon~~ <~~/math~~>

	~~Where~~
	* <~~math> \epsilon_{} </math> is strain~~
	* <math> \epsilon_f </math> is the ~~strain upon failure~~
	* <math> \sigma </math> is stress

	~~Another definition is~~ the ~~ability~~ to ~~absorb mechanical (or kinetic) energy up~~ to ~~failure~~.
	~~The area covered under stress strain curve is called toughness.~~

	~~If the upper limit of integration up~~ to the ~~yield point is restricted, then the energy absorbed per unit volume is known as the [[resilience\|modulus~~ of ~~resilience]]~~.
	~~Mathematically, the modulus~~ of ~~resilience can be expressed by the product~~ of the ~~square of~~ the ~~yield stress divided~~ by ~~two times the Young~~'s ~~modulus~~.

	~~==Toughness tests==~~
	~~Tests can~~ be ~~done~~ by ~~using a pendulum~~ and ~~basic physics~~ to ~~measure how much energy it will hold when released from a particular height~~. ~~By having~~ a ~~sample at~~ the ~~bottom~~ of ~~its swing~~, a ~~measure~~ of ~~toughness can be found, as in the [[Charpy impact test\|Charpy]]~~ and ~~[[Izod impact strength test\|Izod impact tests]]~~.

	~~==Unit of toughness==~~
	~~Tensile toughness (aka ''deformation energy'', ''U''~~<~~sub~~>T<~~/sub~~>~~) is measured in units~~ of [[~~joule]] per [[cube metre]] (J·m<sup>–3<~~/~~sup>) in the [[SI]] system and inch-[[pound-force]] per [[cube inch]] (in·lbf·in<sup>–3<~~/~~sup>) in [[US customary units~~]], ~~''i.e.'' deformation energy per volume of test specimen (merely for gage~~-~~length part)~~.

	~~In terms~~ of ~~[[SI]] system,~~ the ~~unit~~ of ~~tensile toughness can be easily calculated by using area underneath~~ the stress–strain (''σ''–''ε'') curve, which gives tensile toughness value, as given below:<ref>{{cite journal\|author=O.Balkan and H.Demirer\|title=Polym. Compos.\|volume=31\|page=1285\|year=2010\|ISSN=1548-0569}}</ref>

	~~''U''<sub>T</sub> = Area underneath~~ the ~~stress–strain (''σ''–''ε'') curve = ''σ'' × ''ε''~~

	~~''U''<sub>T</sub> = MPa × % = (N·m<sup>−2</sup>·10<sup>6</sup>)·(m·m<sup>–1</sup>·10<sup>–2</sup>)~~

	~~''U''<sub>T</sub> = N·m·m<sup>–3</sup>·10<sup>4</sup>~~

	~~'''''U''<sub>T</sub> = J·m<sup>–3</sup>·10<sup>4</sup>'''~~

	~~==Toughness and strength==~~
	~~Toughness is also defined as area of stress-strain diagram~~ . ~~Toughness is related to the area under the stress-strain curve~~. ~~In order to be tough~~, ~~a material must be both strong~~ and ~~ductile. For example~~, ~~brittle materials (like ceramics) that are strong but with limited ductility are not tough; conversely~~, ~~very ductile materials with low strengths are also not tough. To be tough, a material should withstand both high stresses~~ and ~~high strains~~. ~~Generally speaking, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupturing.~~

	~~==See also==~~
	* [[Fracture toughness]]
	* [[Graph toughness]]
	* [[Hardness]]
	* [[Impact (mechanics)]]
	* [[Resilience]]
	* [[Shock (mechanics)]]
	* [[Tablet hardness testing]]

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Continuum mechanics]]~~
	~~[[Category:Materials science]]~~
	~~[[Category:Physical quantities]]~~

en>David Eppstein: /* See also */ Hawaiian earring

2013-07-14T20:32:42Z

See also: Hawaiian earring

← Older revision		Revision as of 22:32, 14 July 2013
Line 1:		Line 1:
	~~Hello. Let me introduce~~ the ~~author~~. ~~Her~~ name ~~is Refugia Shryock~~. ~~Managing individuals has been his day job~~ for a ~~while~~. ~~For~~ a ~~while she's been in South Dakota~~. ~~The thing she adores most is physique developing~~ and ~~now she is attempting to earn cash with it~~.<br><br>~~Have a look at my page~~: ~~[http~~://~~www~~.~~4gamesonline~~.~~com~~/~~groups~~/~~valuable~~-~~guidance~~-for-~~successfully~~-~~treating-candida-albicans~~/ ~~http:~~//~~www~~.~~4gamesonline~~.~~com/~~]		{{about\|toughness of physical objects\|the mathematical concept in graph theory\|graph toughness}}
			{{refimprove\|date=January 2011}}

			In [[materials science]] and [[metallurgy]], '''toughness''' is the ability of a material to absorb energy and plastically deform without fracturing.<ref name=NDT>[http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Mechanical/Toughness.htm "Toughness"], [http://www.ndt-ed.org/index_flash.htm NDT Education Resource Center], Brian Larson, Editor, 2001-2011, The Collaboration for NDT Education, [[Iowa State University]]</ref>
			One definition of material toughness is the amount of [[energy]] per volume that a material can absorb before [[rupture (engineering)\|rupturing]]. It is also defined as the resistance to [[fracture]] of a material when [[stress (physics)\|stressed]].

			Toughness requires a balance of [[Strength of materials\|strength]] and [[ductility]].<ref name=NDT/>

			==Mathematical definition==
			Toughness can be determined by measuring the area (i.e., by taking the integral) underneath the [[stress-strain curve]]<ref name=NDT/> and its energy of mechanical deformation per unit volume prior to fracture. The explicit mathematical description is:

			: <math> \frac{\mbox{energy}}{\mbox{volume}} = \int_{0}^{\epsilon_f} \sigma\, d\epsilon </math>

			Where
			* <math> \epsilon_{} </math> is strain
			* <math> \epsilon_f </math> is the strain upon failure
			* <math> \sigma </math> is stress

			Another definition is the ability to absorb mechanical (or kinetic) energy up to failure.
			The area covered under stress strain curve is called toughness.

			If the upper limit of integration up to the yield point is restricted, then the energy absorbed per unit volume is known as the [[resilience\|modulus of resilience]].
			Mathematically, the modulus of resilience can be expressed by the product of the square of the yield stress divided by two times the Young's modulus.

			==Toughness tests==
			Tests can be done by using a pendulum and basic physics to measure how much energy it will hold when released from a particular height. By having a sample at the bottom of its swing, a measure of toughness can be found, as in the [[Charpy impact test\|Charpy]] and [[Izod impact strength test\|Izod impact tests]].

			==Unit of toughness==
			Tensile toughness (aka ''deformation energy'', ''U''<sub>T</sub>) is measured in units of [[joule]] per [[cube metre]] (J·m<sup>–3</sup>) in the [[SI]] system and inch-[[pound-force]] per [[cube inch]] (in·lbf·in<sup>–3</sup>) in [[US customary units]], ''i.e.'' deformation energy per volume of test specimen (merely for gage-length part).

			In terms of [[SI]] system, the unit of tensile toughness can be easily calculated by using area underneath the stress–strain (''σ''–''ε'') curve, which gives tensile toughness value, as given below:<ref>{{cite journal\|author=O.Balkan and H.Demirer\|title=Polym. Compos.\|volume=31\|page=1285\|year=2010\|ISSN=1548-0569}}</ref>

			''U''<sub>T</sub> = Area underneath the stress–strain (''σ''–''ε'') curve = ''σ'' × ''ε''

			''U''<sub>T</sub> = MPa × % = (N·m<sup>−2</sup>·10<sup>6</sup>)·(m·m<sup>–1</sup>·10<sup>–2</sup>)

			''U''<sub>T</sub> = N·m·m<sup>–3</sup>·10<sup>4</sup>

			'''''U''<sub>T</sub> = J·m<sup>–3</sup>·10<sup>4</sup>'''

			==Toughness and strength==
			Toughness is also defined as area of stress-strain diagram . Toughness is related to the area under the stress-strain curve. In order to be tough, a material must be both strong and ductile. For example, brittle materials (like ceramics) that are strong but with limited ductility are not tough; conversely, very ductile materials with low strengths are also not tough. To be tough, a material should withstand both high stresses and high strains. Generally speaking, strength indicates how much force the material can support, while toughness indicates how much energy a material can absorb before rupturing.

			==See also==
			* [[Fracture toughness]]
			* [[Graph toughness]]
			* [[Hardness]]
			* [[Impact (mechanics)]]
			* [[Resilience]]
			* [[Shock (mechanics)]]
			* [[Tablet hardness testing]]

			==References==
			{{reflist}}

			[[Category:Continuum mechanics]]
			[[Category:Materials science]]
			[[Category:Physical quantities]]

en>ShelfSkewed: Disambiguate family (mathematics) to indexed family

2012-03-04T04:26:29Z

Disambiguate family (mathematics) to indexed family

New page

Hello. Let me introduce the author. Her name is Refugia Shryock. Managing individuals has been his day job for a while. For a while she's been in South Dakota. The thing she adores most is physique developing and now she is attempting to earn cash with it.<br><br>Have a look at my page: [http://www.4gamesonline.com/groups/valuable-guidance-for-successfully-treating-candida-albicans/ http://www.4gamesonline.com/]