Materials and Structures

, Volume 21, Issue 1, pp 33–40 | Cite as

Mixed-mode fracture toughness testing of concrete beams in three-point bending

  • S. E. Swartz
  • L. W. Lu
  • L. D. Tang


Results obtained for mixed-mode fracture toughness parameters K c , G c , J c , G F (plane strain mixed-mode stress-intensity factor, energy release rate, J-integral and fracture energy, respectively) for small notched concrete beams in bending indicate that all these parameters decrease with x/S (x is the distance from support, S is the span) in general to values near midspan consistent with Mode I results. All the parameters except J c vary with notch depth in a similar manner for each notch location.


Fracture Toughness Fracture Energy Energy Release Rate Crack Mouth Opening Displacement Notch Depth 
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Notch depth, inclined crack length at failure

B, W, L, S

Width, depth, length, span of test beam

E, μ

Modulus of elasticity, Poisson's ratio


Mode I, mixed-mode fracture energy release rates


Fracture energy


Mixed-mode J-integral


Mode I stress-intensity factor


Mode II stress-intensity factor


Mode III stress-intensity factor


Mixed-mode stress-intensity factor


Beam weight between supports


Beam load


Distance from beam support


Crack inclination angle with vertical

\(\bar \delta _0 \)

Load-point displacement at peak load


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Copyright information

© RILEM 1988

Authors and Affiliations

  • S. E. Swartz
    • 1
  • L. W. Lu
    • 2
  • L. D. Tang
    • 3
  1. 1.Department of Civil EngineeringKansas State UniversityManhattanUSA
  2. 2.Department of Civil EngineeringEast-China Jiaotong UniversityJiangxiChina
  3. 3.Department of Agricultural Machinery EngineeringLuoyang Institute of TechnologyLuoyang, HenanChina

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