The effect of ice crystals varies with engine type. The hazard involves large quantities of micro ice particles at high altitude. The previously quoted water/ice densities are like a heavy rain storm at ground level (a strong umbrella required), but with ice crystals there are additional criteria such as density, heat-flow, and ‘stickiness’.
In some engines, the heat flow of the compressor intake-anti icing (inside the engine) might be overwhelmed by the ice mass flow and heat loss. Or more likely result in partial melting enabling the ‘cold’ water to act as a glue to stick ice crystals together (run back ice), resulting in a rapid build-up which chokes the first stages of the compressor (cf pitot problems). The associated changes in air flow may be sensed by the fuel control system which reduces the fuel flow, which results in a reduction in engine speed, which affects the rate of ice build-up – and thence a continuing cycle resulting in ‘rollback’ to idle/sub idle. There may be a point at low rpm where fuel is added (to maintain idle) by the FCU or manual, but the engine is unable to respond and thus the additional fuel increases the engine temp resulting in a further control cycle with a risk of over-temp / stall / shutdown.
Engines may also suffer from ice lumps breaking off with potential damage to later stages of the compressor; and which can affect engine performance after an encounter – even if not detected at the time.
Different engine designs with slightly higher anti-ice heat-flow may protect them in most conditions; similarly an extended compressor intake lip may centrifuge the ‘relatively’ denser crystals (or a significant proportions of them) away from the compressor and exit harmlessly through the fan duct due to fan-whirl – spinner shape, fan design, by-pass duct shape, size, speed, etc.
All of these variables also depend on ice density, duration of exposure, ambient and compressor temperatures according to power setting / aircraft speed.
The safety problem is how to anticipate the combinations in a test program and ensure that you flight test in the appropriate conditions, except you don’t know what appropriate means.
Original designs should cope with a wide range of conditions (cert regs), but then there is longer term exposure to the real atmosphere and real flight operations; – in safety you never fight the war that you train for.
Thus modifications might consider changes to hardware, anti-ice heat flow, or fuel control system – air/fuel flow. And temporarily avoiding the most likely conditions, but with associated risk of human judgement of what is most likely (regulation advisory warning), and adherence to procedures (operator).