Analytical Approaches to Evaluate Residual Cable Lifetime Module 4 Dr. John H. Bickel Evergreen Safety & Reliability Technologies, LLC

Residual Cable Lifetime Assessment Objective is to conservatively demonstrate that should design bases accident occur at end of life conditions, critical equipment will function properly Objective is to conservatively demonstrate that should design bases accident occur at end of life conditions, critical equipment will function properly Demonstration is based on Environmental Qualification program using qualification tests performed on “pre-aged” samples. Demonstration is based on Environmental Qualification program using qualification tests performed on “pre-aged” samples.

“Pre-Aging” Environmental Qualification programs must simulate end of life aged components Environmental Qualification programs must simulate end of life aged components Materials are “pre-aged” before running qualification tests (simulated LOCA tests) Materials are “pre-aged” before running qualification tests (simulated LOCA tests) Elevated temperature/irradiation burn-in tests used prior to qualification tests to simulate cable conditions at end of life. Elevated temperature/irradiation burn-in tests used prior to qualification tests to simulate cable conditions at end of life.

Example EQ Qualification Test Envelope for US BWR Based on Design Basis LOCA

Cable Lifetime Assessments Two predominant failure modes are typically considered: thermal, radiation Two predominant failure modes are typically considered: thermal, radiation Arrhenius thermal aging model Arrhenius thermal aging model Radiation aging via linear dose response model. Radiation aging via linear dose response model. Both need to be considered. Both need to be considered.

Arrhenius Thermal Aging Model From probability theory, mean time to failure is given by: MTTF

Arrhenius Thermal Aging Model Probability density function is assumed to be exponential: Probability density function is assumed to be exponential: f τ (t) = 1/ τ exp (-t/ τ ) With time to failure given by Arrhenius law: With time to failure given by Arrhenius law: τ = k(T) -1 = [A exp (-Φ / kT)] -1 Mean time to failure is simply: Mean time to failure is simply: MTTF = τ = [A exp (-Φ / kT )] -1 k = x eV / °K (Boltzmann’s constant) A, Φ = experimentally derived constants

Arrhenius Thermal Aging Model Effects of aging in elevated temperature environment can be accelerated based on: Effects of aging in elevated temperature environment can be accelerated based on: MTTF 1 = [A exp (-Φ / kT 1 )] -1 MTTF 1 = [A exp (-Φ / kT 1 )] -1 MTTF 2 = [A exp (-Φ / kT 2 )] -1 MTTF 2 = [A exp (-Φ / kT 2 )] -1 Computing the ratio of times to failure yields: Computing the ratio of times to failure yields:

Arrhenius Thermal Aging Model k = x eV / °K (Boltzmann’s constant) k = x eV / °K (Boltzmann’s constant) Φ is an experimentally derived constant that can be obtained from tests of specific materials Φ is an experimentally derived constant that can be obtained from tests of specific materials Φ is more commonly assumed at low value: 0.5eV when specific material test data is not available Φ is more commonly assumed at low value: 0.5eV when specific material test data is not available Lower values of Φ are conservative Lower values of Φ are conservative Unjustified use of larger Φ values can be major source of error Unjustified use of larger Φ values can be major source of error

Comparison of Activation Energies Plot below shows effect of Plot below shows effect of Φ = 0.5 vs. 1.0 eV

Applications of Thermal Aging Model It is desired to qualify electrical cable that will operate in a non-radiation environment at no hotter than 40°C ( °K) for a 40 year lifetime (350,400 hours). It is desired to qualify electrical cable that will operate in a non-radiation environment at no hotter than 40°C ( °K) for a 40 year lifetime (350,400 hours). How long should a thermal qualification test run (at different temperatures) to demonstrate cable is qualified for such environment? How long should a thermal qualification test run (at different temperatures) to demonstrate cable is qualified for such environment?

Applications of Thermal Aging Model

Based on operating experience temperatures have never exceeded 30°C ( °K) Based on operating experience temperatures have never exceeded 30°C ( °K) After 30 years of operation, it is desired to demonstrate that cable is capable of functioning for 30 more years (e.g. 60 years – or 525,600 hours) based on lower temperatures. After 30 years of operation, it is desired to demonstrate that cable is capable of functioning for 30 more years (e.g. 60 years – or 525,600 hours) based on lower temperatures. Is this justifiable? Is this justifiable?

Applications of Thermal Aging Model MTTF 2 = 350,400 hours at 40°C ( °K) MTTF 2 = 350,400 hours at 40°C ( °K) Solving for MTTF 1 at 30°C ( °K) yields: Solving for MTTF 1 at 30°C ( °K) yields: MTTF 1 = 645,700 hours vs. 525,600 hours MTTF 1 = 645,700 hours vs. 525,600 hours It is justifiable. It is justifiable.

Radiation Aging Model Linear Dose vs. Effects is assumed Linear Dose vs. Effects is assumed Damage = Dose (Rads) x Time (hours) Damage = Dose (Rads) x Time (hours) Simulate effects of 40 year plant lifetime by use of higher qualification dose rates Simulate effects of 40 year plant lifetime by use of higher qualification dose rates t 1 = (D 2 /D 1 ) x t 2 is used for scaling t 1 = (D 2 /D 1 ) x t 2 is used for scaling

Application of Radiation Aging Model 40 year dose to equipment ~ 4.5 x 10 7 Rads 40 year dose to equipment ~ 4.5 x 10 7 Rads ( or: 4.5 x 10 5 Gy) To run accelerated aging test to cope with radiation effects, how large a dose is required? To run accelerated aging test to cope with radiation effects, how large a dose is required?

Application of Radiation Aging Model