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ASTM D 123 describes as follows

Abrasion, n---the wearing away of any part of a material by rubbing against another surface.

ASTM also has prescribed several methods to quantify abrasion resistance of textile materials these tests are

ASTM D 4966 -- 98 Standard Test Method for Abrasion Resistance of Textile Fabrics (Martindale Abrasion Tester Method)

ASTM D 3884 Test Method for Abrasion Resistance of Textile Fabrics (Rotary Platform, Double-Head Method)3

ASTM D 3885 Test Method for Abrasion Resistance of Textile Fabrics (Flexing and Abrasion Method)3

ASTM D 3886 Test Method for Abrasion Resistance of Textile Fabrics (Inflated Diaphragm Method)3

ASTM D 4157 Test Method for Abrasion Resistance of Textile Fabrics (Oscillatory Cylinder Method)3

ASTM D 4158 Test Method for Abrasion Resistance of Textile Fabrics (Uniform Abrasion Method)3

AATCC Test Method 93 Abrasion Resistance of Fabrics: Accelerator Method4

In All of the above materials the tested specimen is rubbed is a particular manner against an abradent which may be a fabric, or a emery sheet or like for either a certain amount of time for for a certain number of strokes or cycles.

At the end of the testing period , any change that may occur to the tested specimen normally 3 types of changes are looked for

1. Mass Loss
2. Color Change
3. Hole formation or yarn breakage

The Earlier these changes occur the poorer the resistance to abrasion.

Factors loke thickness of fabric, piles, any pretreatment to reduce or increace surface friction , etc all have a profound effect on the Abrasion resistance.

In real life, trousers in case of apparel and Upholstery are subject to more abrasion than fabrics used in any other domestic use. In case of fabrics used for industrial application like belts etc are required to have very high abrasion resistance.

References
ASTM International Book of Standards Volume 7.01 and 7.02
AATCC Technical Manual - 2009
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Q: What is a typical textile abrasion resistance?
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