Sun kink refers to a condition that can occur on hot days in rail tracks

Rail tracks

The track on a railway or railroad, also known as the permanent way, is the structure consisting of the rails, fasteners, sleepers and ballast , plus the underlying subgrade...

. The phenomenon is caused by what is properly termed as buckling

Buckling

In science, buckling is a mathematical instability, leading to a failure mode.Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium...

.

The buckling force

Force

In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

 in the track due to warming up is a function

Function (mathematics)

In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

 of the rise in temperature only and is independent of the track length: .

Derivation of buckling force function:

The linear thermal expansion Thermal expansion Thermal expansion is the tendency of matter to change in volume in response to a change in temperature.When a substance is heated, its particles begin moving more and thus usually maintain a greater average separation. Materials which contract with increasing temperature are rare; this effect is...  due to heating of the track is found using where ΔL = thermal expansion of the rail L = length of the rail/track α = coefficient of thermal expansion ΔT = increase in temperature According to Hooke's law Hooke's law In mechanics, and physics, Hooke's law of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load applied to it. Many materials obey this law as long as the load does not exceed the material's elastic limit. Materials for which Hooke's law...  the extension due to a force (in the rail) is where ΔL = extension of the rail/track F = the force extending a rod, here the induced force in the rail E = modulus of elasticity of rail material (steel) A = cross section of rail L = length of rail Putting these together gives or

Earthquakes

Earthquake

Earthquake

An earthquake is the result of a sudden release of energy in the Earth's crust that creates seismic waves. The seismicity, seismism or seismic activity of an area refers to the frequency, type and size of earthquakes experienced over a period of time...

s can also cause track to buckle. If the ground is compressed, a buckle occurs, while if the ground is stretched, the rails can break leaving a gap.

Accidents

These accidents were deemed to be sun kink related (more information available at List of rail accidents (2000–2009)):

• April 18, 2002 Amtrak
  Amtrak
  The National Railroad Passenger Corporation, doing business as Amtrak , is a government-owned corporation that was organized on May 1, 1971, to provide intercity passenger train service in the United States. "Amtrak" is a portmanteau of the words "America" and "track". It is headquartered at Union...
  
   Auto-Train derailment, off CSX tracks, near Crescent City, Florida
  Crescent City, Florida
  Crescent City is a city in Putnam County, Florida, United States. The city is located on two lakes and is part of the Palatka Micropolitan Statistical Area. Crescent Lake lies to the east of town and Lake Stella is located to the west.-Geography:...
  
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• July 29, 2002 Amtrak
  Amtrak
  The National Railroad Passenger Corporation, doing business as Amtrak , is a government-owned corporation that was organized on May 1, 1971, to provide intercity passenger train service in the United States. "Amtrak" is a portmanteau of the words "America" and "track". It is headquartered at Union...
  
   Capitol Limited derails, off CSX tracks, near Kensington, Maryland
  Kensington, Maryland
  Kensington is a town in Montgomery County, Maryland, United States. The population was 1,873 at the 2000 census. Greater Kensington encompasses the entire 20895 zip code and its population is an order of magnitude larger than that of the town at its center....
  
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• July 8, 2010 CSX train derails off tracks in Waxhaw, North Carolina
  Waxhaw, North Carolina
  Waxhaw is a town located in Union County, North Carolina. The population was 2,627 at the 2000 Census.-Geography:Waxhaw is located at .According to the United States Census Bureau, the town has a total area of , all of it land...
  
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