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" Toughness requires a balance of strength and ductility.
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" Toughness can be determined by integrating the stress-strain curve. It is the energy of mechanical deformation per unit volume prior to fracture. The explicit mathematical description is:
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" where
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" Another definition is the ability to absorb mechanical energy up to the point of failure. The area under the stress-strain curve is called toughness.
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" If the upper limit of integration up to the yield point is restricted, the energy absorbed per unit volume is known as the 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 of elasticity. That is,
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" The toughness of a material can be measured using a small specimen of that material. A typical testing machine uses a pendulum to strike a notched specimen of defined cross-section and deform it. The height from which the pendulum fell, minus the height to which it rose after deforming the specimen, multiplied by the weight of the pendulum is a measure of the energy absorbed by the specimen as it was deformed during the impact with the pendulum. The Charpy and Izod notched impact strength tests are typical ASTM tests used to determine toughness.
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" Tensile toughness (or, ""deformation energy"", ""U"") is measured in units of joule per cubic metre (J·m) in the SI system and inch-pound-force per cubic inch (in·lbf·in) in US customary units.
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" 1.00 N·m.m ≃  in·lbf·in and 1.00 in·lbf·in ≃ 6.89 kN·m.m.
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" In the 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:
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" Toughness can also be defined with respect to regions of a 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.
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"= = = Snooker world rankings 1993/1994 = = =
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" Snooker world rankings 1993/1994: The professional world rankings for the top 64 snooker players in the 1993/1994 season are listed below.
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"= = = Guyandotte River = = =
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" The Guyandotte River is a tributary of the Ohio River, approximately 166 mi (267 km) long, in southwestern West Virginia in the United States. It was named after the French term for the Wendat Native Americans. It drains an area of the unglaciated Allegheny Plateau south of the Ohio between the watersheds of the Kanawha River to the northeast and Twelvepole Creek and the Big Sandy River to the southwest. Via the Ohio River, it is part of the Mississippi River watershed.
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" The Guyandotte River is formed in southwestern Raleigh County by the confluence of three streams, Winding Gulf, Stonecoal Creek, and the Devils Fork. and flows initially west-northwestwardly into Wyoming and Mingo counties. It turns briefly northward in Mingo County and enters Logan County, where it turns north-northwestwardly for the remainder of its highly meandering course through Logan, Lincoln and Cabell counties. It enters the Ohio River from the south at Huntington, about 5 mi (8 km) east of the city's downtown.
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" A U.S. Army Corps of Engineers dam in Mingo County causes the river to widen as R.D. Bailey Lake in Mingo and western Wyoming Counties.
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" The Mud River joins the Guyandotte at Barboursville in Cabell County. The Slab Fork joins the Guyandotte in downtown Mullens in Wyoming County. Big Ugly Creek joins the Guyandotte in Lincoln County.
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" In Mullens, an active watershed organization is working to reduce pollution in the headwaters of the Guyandotte River. The Upper Guyandotte Watershed Association (UGWA) is a grassroots, community-based organization working to reduce sources of pollution in order to clean up streams and make the watershed a better place to live. UGWA has garnered much public support and produced results in partnering with numerous local, state, and federal agencies.
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" According to the Geographic Names Information System (GNIS), the Guyandotte River has also been known as:
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"= = = University of Engineering and Technology, Lahore = = =
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" The University of Engineering and Technology, Lahore (UET Lahore) is a public university located in Lahore, Punjab, Pakistan specializing in science, technology, engineering and mathematics (STEM) subjects. It is the oldest and one of the most selective engineering institutions in Pakistan.
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" Founded in 1921 as Mughalpura Technical College, it later became the 'MacLagan Engineering College', a name given to it in 1923 when Sir Edward Douglas MacLagan, the then Governor of Punjab who laid the foundation stone of the main building, now called the Main Block.
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" In 1932, it was affiliated with the University of the Punjab for an award of a Bachelor's Degree in Engineering.
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" In 1962, it was granted charter in 1962 and was named as the West Pakistan University of Engineering and Technology, Lahore.
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" In 1972, it was officially renamed as the University of Engineering and Technology, Lahore. A second campus of the university was established in 1975 in Sahiwal which was relocated in Taxila in 1978 and became an independent university in 1993 called University of Engineering and Technology, Taxila.
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" The university, as of 2016, has a faculty of 881 people with 257 with doctorates. It has a total of 9,385 undergraduate and 1,708 postgraduate students studying. It has a strong collaboration with University of South Carolina, University of Manchester and the Queen Mary University of London and has conducted research funded by Huawei, Cavium Networks, Microsoft and MontaVista. It is one of the highest ranked universities in Pakistan with domestic rankings placing it as the fifth best engineering school in Pakistan while QS World University Ranking putting U.E.T as 701st in the world every year between 2013 and 2016. It is also ranked as #701 in world by the same publication in 2018.
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" In 2018 QS rankings university observed downgrading from 701 to among 801–1000 ranked slot. Meanwhile, in Asia university ranking is currently being ranked at #200 and in world wide unverisity ranking is 701.
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" The university was established in 1921 in Mughalpura, a suburban area of Lahore, as Mughalpura Technical College. In 1923, the name was changed to Maclagan Engineering College to honor Sir Edward Maclagan, then Governor of the Punjab, who laid the foundation stone of the building.
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" In 1932, the institution became affiliated with the University of the Punjab for awarding a bachelor's degree in engineering. By the time of independence in 1947, it offered B.Sc. degrees in electrical, mechanical and civil engineering.
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" In 1954, a bachelor's degree program in mining engineering was started. In 1962, it was upgraded to West Pakistan University of Engineering and Technology. During the 1960s, bachelor's degree programs were started in chemical engineering, petroleum and gas engineering, metallurgical engineering, architecture and city and regional planning. By the 1970s, it had established over a score of master's degree programs in engineering, architecture, city and regional planning and allied disciplines. Several Ph.D. degree programs were also started. Today, it is widely considered one of the best and most prestigious engineering university of Pakistan where more than 50,000 students apply for admission every year.
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" The campus is situated on the Grand Trunk Road (GT Road), few kilometers from the Mughal era Shalimar Gardens.
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" The university consists of following faculties and departments:
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" The university consists of following research centers:
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" More than 870 students are foreign students and more than 1000 are female students.
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" The UET faculty consists of 741 people including 14 international faculty members; around 122 have doctoral degrees. Its faculty holds one Tamgha-e-Imtiaz, one Sitara-i-Imtiaz, one Izaz-e-Kamal Presidential Award and nine HEC Best Teacher Awards.
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" The university has established a Directorate of Research, Extension and Advisory Services which strives for the promotion and organization of research activities. The Al-Khwarizmi Institute of Computer Sciences is a notable name in research activity in computer sciences in Pakistan.
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" The university has a sports complex, consisting of a swimming pool, tennis court, table tennis court, squash court and a cricket stadium that is also used for athletics. The university has several football grounds. Apart from sports-related facilities, there are societies to promote co-curricular activities. These include:
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" The National Library of Engineering Science, inaugurated by Faisal bin Abdul-Aziz Al Saud, is the central library of the university with a seating capacity for 400 readers and more than 125,000 volumes of books, 22,000 volumes of bound serials and 600 issues of scientific and technical serials on diverse fields. The Library has the honour of having recently been chosen by the Higher Education Commission to serve as the primary resource center for engineering and technical education. It is a three-story building in front of Allah Hu Chowk.
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"= = = Snooker world rankings 1992/1993 = = =
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" Snooker world rankings 1992/1993: The professional world rankings for the top 32 snooker players and two others from the top 64 in the 1992/1993 season are listed below.
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"= = = Zapata: El sueño de un héroe = = =