Lightweight phase-field surrogate for modelling ductile-to-brittle transition through phenomenological elastoplastic coupling

TL;DR

This paper introduces a lightweight phase-field surrogate model that efficiently captures the ductile-to-brittle transition in materials at cryogenic temperatures by incorporating temperature-dependent phenomenological mechanisms, enabling systematic simulations.

Contribution

The work presents a novel, computationally efficient surrogate model for DBT that integrates temperature-dependent phenomenological mechanisms within a phase-field framework, implemented in FEniCSx.

Findings

Model captures transition from ductile to brittle response with temperature change.

Simulations show reduced displacement to fracture at lower temperatures.

Transition trends are robust across different interpolation schemes.

Abstract

The ductile-to-brittle transition (DBT) in body-centred cubic systems is a central design constraint for cryogenic structures. Performing parametric studies to enhance the understanding on DBT using fully coupled thermomechanical continuum DBT models is computationally expensive. Therefore, in this work, a lightweight phase-field surrogate is proposed. This surrogate approach captures key \emph{DBT-like} trends within a standard isothermal two-field (displacement--damage) setting by prescribing temperature dependence through three phenomenological mechanisms: (i) a temperature-dependent degradation exponent $n(T)$ that sharpens stiffness loss from gradual (ductile-like, $n=2.0$ at 293\,K) to abrupt (brittle-like, $n=3.5$ at 77\,K), (ii) temperature-dependent yield stress and elastic modulus to modulate the balance between plastic dissipation and elastic energy storage, and (iii) an effective fracture toughness and driving-force scaling to represent reduced crack-tip shielding at cryogenic temperatures. The model is implemented in FEniCSx using small-strain $J_2$ return mapping and a staggered solution scheme. Simulations of a single-edge-notched specimen over 77--293\,K demonstrate a systematic progression from brittle-like to ductile-like response, characterised by reduced displacement to unstable fracture, a transition from abrupt post-peak load drop to extended softening, and a shift from narrow, localised damage bands with confined plasticity to broader process zones. A sensitivity study comparing four interpolation schemes (linear, smoothstep, exponential, hybrid) shows that the qualitative transition trends are robust, with interpolation primarily affecting intermediate-temperature responses while endpoint behaviours remain unchanged.