[Paper Review] Damage and Healing in Fatigue Fracture

Ferenc Kun, M. H. A. S. Costa+5 more|arXiv (Cornell University)|Jul 24, 2006

Asphalt Pavement Performance Evaluation1 references3 citations

TL;DR

This paper proposes a fiber bundle model (FBM) and a fuse model (RFM) to explain fatigue fracture in asphalt under cyclic compression, incorporating damage accumulation and microcrack healing. It reveals universal scaling laws with a critical memory threshold τ_c, where lifetime diverges as (τ - τ_c)^{-δ} with δ = 0.5, and establishes a finite fatigue limit below which failure does not occur, validated by experiments showing a Basquin law with exponent α = 2.2.

ABSTRACT

We present an experimental and theoretical study of the fatigue failure of asphalt under cyclic compression. Varying the load amplitude, experiments reveal a finite fatigue limit below which the specimen does not break, while approaching the tensile strength of the material a rapid failure occurs. In the intermediate load range, the lifetime decreases with the load as a power law. We introduce two novel theoretical approaches, namely, a fiber bundle model and a fuse model, and show that both capture the major microscopic mechanisms of the fatigue failure of asphalt, providing an excellent agreement with the experimental findings. Model calculations show that the competition of damage accumulation and healing of microcracks gives rise to novel scaling laws for fatigue failure.

Motivation & Objective

• To understand the microscopic mechanisms behind fatigue failure in asphalt under cyclic loading, particularly the interplay between damage accumulation and healing.
• To develop theoretical models that quantitatively reproduce experimental fatigue life data, including the existence of a fatigue limit.
• To identify universal scaling laws arising from the competition between microcrack nucleation and healing in disordered materials.
• To explain the power-law dependence of fatigue lifetime on load amplitude (Basquin law) and the emergence of a finite fatigue limit.
• To investigate how healing—controlled by a finite memory range τ—leads to a critical threshold τ_c where lifetime diverges.

Proposed method

• Adapted the fiber bundle model (FBM) to simulate fatigue in asphalt, where fibers fail irreversibly under load, with damage accumulation modeled by a cumulative damage variable c(t).
• Incorporated healing by introducing a finite memory range τ, where microcracks can recover if the load is below a threshold, modeled via a time-dependent recovery mechanism.
• Used the random fuse model (RFM) with history-dependent ageing, where fuses accumulate damage only when current exceeds a threshold i₀, capturing finite activation energy for crack nucleation.
• Defined the ageing variable A(t) = Σₜ′=1ᵗ a(i(t′) - i₀)^γ, where fuses fail when A(t) > A_max, with A_max drawn from a uniform distribution.
• Solved Kirchhoff’s equations numerically to compute current redistribution after each fuse failure, simulating progressive damage in the network.
• Analyzed the lifetime N_f as a function of load σ₀/σ_c and memory range τ, identifying critical behavior near τ_c through power-law scaling.

Experimental results

Research questions

• RQ1 How does the competition between microcrack nucleation and healing affect the fatigue lifetime in asphalt under cyclic loading?
• RQ2 What is the origin of the experimentally observed finite fatigue limit below which no failure occurs?
• RQ3 Does the system exhibit universal scaling behavior near the critical memory range τ_c where lifetime diverges?
• RQ4 How do the scaling exponents of fatigue failure depend on disorder distribution and damage accumulation mechanisms?
• RQ5 Can the Basquin law (N_f ∼ (σ₀/σ_c)^{-α}) be derived from microscopic models that include healing and finite activation thresholds?

Key findings

• The experimental fatigue lifetime N_f follows a Basquin law with exponent α = 2.2 ± 0.1 in the intermediate load regime, confirming power-law scaling.
• A finite fatigue limit σ_l exists below which the specimen does not fail, corresponding to a critical load where lifetime diverges.
• In the FBM, the lifetime diverges as (τ - τ_c)^{-δ} with δ = 0.5 ± 0.01, a universal exponent independent of disorder type or γ.
• The critical memory threshold τ_c separates regimes of finite and infinite lifetime, with healing dominating below τ_c.
• The fuse model (RFM) with a finite activation threshold i₀ reproduces the same three-regime behavior: rapid failure, Basquin scaling, and a fatigue limit.
• The exponent in the Basquin regime matches the damage accumulation exponent γ in the RFM, confirming the model’s consistency with experimental data.