Editing Composite material (section)

=== Particle reinforcement ===
In general, particle reinforcement is [[strengthening mechanisms of materials|strengthening]] the composites less than [[fiber]] reinforcement. It is used to enhance the [[stiffness]] of the composites while increasing the [[yield (engineering)|strength]] and the [[toughness]]. Because of their [[mechanical properties]], they are used in applications in which [[wear]] resistance is required. For example, hardness of [[engineered cementitious composite|cement]] can be increased by reinforcing gravel particles, drastically. Particle reinforcement a highly advantageous method of tuning mechanical properties of materials since it is very easy implement while being low cost.<ref>{{cite journal |last1=Wu |first1=Xiangguo |last2=Yang |first2=Jing |last3=Mpalla |first3=Issa B. |title=Preliminary design and structural responses of typical hybrid wind tower made of ultra high performance cementitious composites |journal=Structural Engineering and Mechanics |date=25 December 2013 |volume=48 |issue=6 |pages=791–807 |doi=10.12989/sem.2013.48.6.791 }}</ref><ref>{{cite journal |last1=Li |first1=Mo |last2=Li |first2=Victor C. |title=Rheology, fiber dispersion, and robust properties of Engineered Cementitious Composites |journal=Materials and Structures |date=March 2013 |volume=46 |issue=3 |pages=405–420 |doi=10.1617/s11527-012-9909-z |hdl=2027.42/94214 |hdl-access=free }}</ref><ref>{{cite journal |date=2008 |title=Large-Scale Processing of Engineered Cementitious Composites |journal=ACI Materials Journal |volume=105 |issue=4 |doi=10.14359/19897 }}</ref><ref>{{cite journal |last1=Zeidi |first1=Mahdi |last2=Kim |first2=Chun IL |last3=Park |first3=Chul B. |date=2021 |title=The role of interface on the toughening and failure mechanisms of thermoplastic nanocomposites reinforced with nanofibrillated rubbers |journal=Nanoscale |volume=13 |issue=47 |pages=20248–20280 |doi=10.1039/D1NR07363J |pmid=34851346 }}</ref>

The [[elastic modulus]] of particle-reinforced composites can be expressed as,
:<math>E_c = V_m E_m + K_c V_p E_p</math>

where E is the [[elastic modulus]], V is the [[volume fraction]]. The subscripts c, p and m are indicating composite, particle and matrix, respectively. <math>K_c</math> is a constant can be found empirically.

Similarly, tensile strength of particle-reinforced composites can be expressed as,
:<math>(T.S.)_c = V_m (T.S.)_m + K_s V_p (T.S.)_p</math>

where T.S. is the [[Ultimate tensile strength|tensile strength]], and <math>K_s</math> is a constant (not equal to <math>K_c</math>) that can be found empirically.