Finite Element/Fracture Mechanics

MPM offers a wide range of analytical and experimental services in the fields of applied mechanics and fracture mechanics.  In addition to finite element and elastic/elastic-plastic fracture analyses, MPM's laboratory capabilities can be used to verify model predictions and to test theories by building prototypes.

Thermal And Stress

MPM employs a variety of numerical and analytical methods for the thermal and stress analysis of equipment and structures.  General purpose commercial software such as ABAQUS or ADINA can be used or, when appropriate, special purpose proprietary software such as WELD3 and DYN3D can be used.  Linear elastic, elastic-plastic, and visco-plastic material behavior can be analyzed.  Loading can be thermal, static, or dynamic.

Fracture Mechanics Analysis

Fracture mechanics analysis is used to understand crack growth and fracture behavior.  Crack growth behavior due to fatigue, stress corrosion, creep, or some combination thereof can be simulated and predicted with the appropriate software and experimental data.  Fracture occurs when a crack reaches its critical size.  The critical crack size depends on the material's temperature dependent fracture toughness, the location and orientation of the crack, and the applied loads.  Fracture can involve very little plastic deformation (brittle fracture) or very significant plastic deformation (ductile fracture).  If the material has very high fracture toughness properties, the final failure may be due to plastic collapse rather than fracture.  Due to the inherent complexities, fracture mechanics analyses often involve the use of more than one software tool.  Simulation of crack growth via fatigue, stress corrosion, or creep typically requires the use of special purpose software.  On the other hand, general purpose finite element thermal and stress analysis software can often be used to calculate critical crack sizes.  However, special purpose proprietary software such as ALT3D can sometimes provide significant advantages over general purpose finite element software, even in the critical crack size calculations.  With the wide range of analysis capabilities available, MPM can tailor the analysis approach to the special requirements of the problem.  This results in greater accuracy and efficiency.

Welding Analysis

Many equipment and structural failures occur in or near weld joints.  These failures can be due to poor weld design but are more often due to weld defects and/or a sensitivity of the weld material to fatigue or stress corrosion cracking.  A common third factor in weld failures is that weld materials often exhibit lower fracture toughness than the neighboring base metal.  Fatigue and stress corrosion cracking behavior are affected by residual stresses as well as applied service loads.  Since the welding process typically leaves residual stresses that are on the order of the material's yield stress in or near the weld, any analysis of crack growth must include the effects of these stresses.  MPM can use the proprietary WELD3 finite element software to simulate the welding process and to calculate residual welding stresses.  These residual stresses are typically a key input to weld fracture mechanics analysis.

Neutron Transport Analysis

Nuclear power plants contain surveillance capsules with neutron dosimeters and mechanical property test specimens.  These capsules are pulled periodically throughout the life of the plant to monitor the properties of the pressure vessel.  When the capsules are analyzed, a neutron transport analysis is performed to determine the neutron fluence to the capsule and the vessel and to compare the calculated results with the dosimetry measurements.  In addition, neutron transport analyses are needed in other cases where the fluence to a primary system component may affect the in-service performance of the component.  Examples include BWR shrouds and PWR vessel internal components.

Transport Model Description

MPM capabilities include calculation of neutron transport for a wide variety of geometries of interest.  For typical cases where the locations of interest are within the reactor beltline region, synthesis of two dimensional calculations can be carried out using discrete ordinates transport methods.  The DORT code is selected for these analyses because of the ease of use, speed of calculations, and routine acceptance by the Nuclear Regulatory Commission (NRC).  MPM uses the latest cross section libraries and the calculations fully satisfy the requirements of NRC Regulatory Guide 1.190, "Calculational and Dosimetry Methods for Determining Pressure Vessel Neutron Fluence".  In more complex cases, three dimensional discrete ordinates or Monte Carlo transport calculations can be carried out. 

P-T Curve Analysis

Pressure-Temperature (P-T) operating curves are required to ensure safe operation of pressure vessels.  The regulations governing the calculation of P-T curves for nuclear power plants are found in the Code of Federal Regulations (CFR), the ASME Boiler and Pressure Vessel Code, and Nuclear Regulatory Commission (NRC) Regulatory Guides.  The fracture toughness requirements for the pressure vessel for testing and operational conditions are specified in Section IV of 10 CFR 50, Appendix G.  This appendix requires implementation of the acceptance and performance criteria of Appendix G to Section III of the Code.  Appendix G to 10 CFR 50 requires that the effects of neutron irradiation on the nil ductility reference temperature of the vessel beltline materials must be included in the P-T curve calculations.  Surveillance capsules are periodically pulled and analyzed to monitor neutron damage to the vessel.  In most cases, the P-T curves must be updated after the capsule analysis has been completed.

P-T Curve Software

MPM has developed PT Curve™ v2.0 to perform the calculations required to determine the allowable loadings on the reactor pressure vessel during heat up, cool down, and leak/hydro testing.  PT Curve™ v2.0 has been Quality Assurance (QA) verified in accordance with 10 CFR 50, Appendix B under the MPM Nuclear Quality Assurance Program.  The calculations and models of PT Curve™ v2.0 are based on years of experience obtained by MPM and the result is accurate and conservative P-T curves which have been approved by the Nuclear Regulatory Commission (NRC) in numerous submittals.  The key features of the model are summarized below:

  • Limiting adjusted nil-ductility reference temperature in accordance with NRC Regulatory Guide 1.99
  • Thermal transient heat transfer analysis to determine thermal loads
  • Instrument errors are accounted for in a conservative manner
  • If it is beneficial, Code Case N-640 (approved by ASME in 1997), which allows KIc to be used in place of KIa as the reference fracture toughness, can be implemented
  • If applicable, Code Case N-588 can be used.  This code case allows for the assumption of circumferential cracks if considering weld metal in a circumferential weld.  This code case is beneficial to the final P-T curves primarily if the limiting material is in a circumferential weld.